Find original functions from a composite function [on hold] The 2019 Stack Overflow Developer Survey Results Are InComposite functions and one to oneFinding range of transformation of function from range of originalHow to find the original function from a definite integral.How to find composite functions upto infinity for a given function?Behaviour of composition functions of a composite functionFunctions propertiesCan't figure out this odd functionComposite function simple questionMore on periodic functions - from 100 periodic functionsfinding an outside function given composite function

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Find original functions from a composite function [on hold]



The 2019 Stack Overflow Developer Survey Results Are InComposite functions and one to oneFinding range of transformation of function from range of originalHow to find the original function from a definite integral.How to find composite functions upto infinity for a given function?Behaviour of composition functions of a composite functionFunctions propertiesCan't figure out this odd functionComposite function simple questionMore on periodic functions - from 100 periodic functionsfinding an outside function given composite function










2












$begingroup$


I have the following problem that I am stuck on:



$ f(g(x))=2^x+5 $



and I must find $f(x)$ and $g(x)$



Can anyone help?










share|cite|improve this question









New contributor




Daniel Amaral is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$



put on hold as off-topic by Eevee Trainer, Leucippus, Lord Shark the Unknown, Robert Shore, José Carlos Santos Apr 8 at 9:07


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, Leucippus, Robert Shore, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.















  • $begingroup$
    $fg$ is the product of $f,g$ or their composition?
    $endgroup$
    – Shubham Johri
    Apr 7 at 18:20










  • $begingroup$
    It is their composition. Also, it is 2 to the power of (x+5). Sorry I am new here I wasn't really sure how to make it like that.
    $endgroup$
    – Daniel Amaral
    Apr 7 at 18:21






  • 4




    $begingroup$
    You should probably add more context, this way it is not clear for what do you want this, for example $g(x)=x$ and $f(x)=2^x+5$ would satisfy your requirements, but I doubt it is of any use.
    $endgroup$
    – Sil
    Apr 7 at 18:22











  • $begingroup$
    In other words, there are infinitely many solutions to your problem. Consider $f(x)=2^nx+5,g(x)=x/n$.
    $endgroup$
    – Shubham Johri
    Apr 7 at 18:24










  • $begingroup$
    Well that's really all that was in the question. Basically it said the expression for the composition of f(x) and g(x) is that, and it asked to find expressions for f(x) and g(x)
    $endgroup$
    – Daniel Amaral
    Apr 7 at 18:25















2












$begingroup$


I have the following problem that I am stuck on:



$ f(g(x))=2^x+5 $



and I must find $f(x)$ and $g(x)$



Can anyone help?










share|cite|improve this question









New contributor




Daniel Amaral is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$



put on hold as off-topic by Eevee Trainer, Leucippus, Lord Shark the Unknown, Robert Shore, José Carlos Santos Apr 8 at 9:07


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, Leucippus, Robert Shore, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.















  • $begingroup$
    $fg$ is the product of $f,g$ or their composition?
    $endgroup$
    – Shubham Johri
    Apr 7 at 18:20










  • $begingroup$
    It is their composition. Also, it is 2 to the power of (x+5). Sorry I am new here I wasn't really sure how to make it like that.
    $endgroup$
    – Daniel Amaral
    Apr 7 at 18:21






  • 4




    $begingroup$
    You should probably add more context, this way it is not clear for what do you want this, for example $g(x)=x$ and $f(x)=2^x+5$ would satisfy your requirements, but I doubt it is of any use.
    $endgroup$
    – Sil
    Apr 7 at 18:22











  • $begingroup$
    In other words, there are infinitely many solutions to your problem. Consider $f(x)=2^nx+5,g(x)=x/n$.
    $endgroup$
    – Shubham Johri
    Apr 7 at 18:24










  • $begingroup$
    Well that's really all that was in the question. Basically it said the expression for the composition of f(x) and g(x) is that, and it asked to find expressions for f(x) and g(x)
    $endgroup$
    – Daniel Amaral
    Apr 7 at 18:25













2












2








2





$begingroup$


I have the following problem that I am stuck on:



$ f(g(x))=2^x+5 $



and I must find $f(x)$ and $g(x)$



Can anyone help?










share|cite|improve this question









New contributor




Daniel Amaral is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$




I have the following problem that I am stuck on:



$ f(g(x))=2^x+5 $



and I must find $f(x)$ and $g(x)$



Can anyone help?







functions






share|cite|improve this question









New contributor




Daniel Amaral is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question









New contributor




Daniel Amaral is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




share|cite|improve this question








edited Apr 7 at 18:22









Arthur

123k7122211




123k7122211






New contributor




Daniel Amaral is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked Apr 7 at 18:19









Daniel AmaralDaniel Amaral

163




163




New contributor




Daniel Amaral is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Daniel Amaral is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Daniel Amaral is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




put on hold as off-topic by Eevee Trainer, Leucippus, Lord Shark the Unknown, Robert Shore, José Carlos Santos Apr 8 at 9:07


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, Leucippus, Robert Shore, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.







put on hold as off-topic by Eevee Trainer, Leucippus, Lord Shark the Unknown, Robert Shore, José Carlos Santos Apr 8 at 9:07


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, Leucippus, Robert Shore, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.











  • $begingroup$
    $fg$ is the product of $f,g$ or their composition?
    $endgroup$
    – Shubham Johri
    Apr 7 at 18:20










  • $begingroup$
    It is their composition. Also, it is 2 to the power of (x+5). Sorry I am new here I wasn't really sure how to make it like that.
    $endgroup$
    – Daniel Amaral
    Apr 7 at 18:21






  • 4




    $begingroup$
    You should probably add more context, this way it is not clear for what do you want this, for example $g(x)=x$ and $f(x)=2^x+5$ would satisfy your requirements, but I doubt it is of any use.
    $endgroup$
    – Sil
    Apr 7 at 18:22











  • $begingroup$
    In other words, there are infinitely many solutions to your problem. Consider $f(x)=2^nx+5,g(x)=x/n$.
    $endgroup$
    – Shubham Johri
    Apr 7 at 18:24










  • $begingroup$
    Well that's really all that was in the question. Basically it said the expression for the composition of f(x) and g(x) is that, and it asked to find expressions for f(x) and g(x)
    $endgroup$
    – Daniel Amaral
    Apr 7 at 18:25
















  • $begingroup$
    $fg$ is the product of $f,g$ or their composition?
    $endgroup$
    – Shubham Johri
    Apr 7 at 18:20










  • $begingroup$
    It is their composition. Also, it is 2 to the power of (x+5). Sorry I am new here I wasn't really sure how to make it like that.
    $endgroup$
    – Daniel Amaral
    Apr 7 at 18:21






  • 4




    $begingroup$
    You should probably add more context, this way it is not clear for what do you want this, for example $g(x)=x$ and $f(x)=2^x+5$ would satisfy your requirements, but I doubt it is of any use.
    $endgroup$
    – Sil
    Apr 7 at 18:22











  • $begingroup$
    In other words, there are infinitely many solutions to your problem. Consider $f(x)=2^nx+5,g(x)=x/n$.
    $endgroup$
    – Shubham Johri
    Apr 7 at 18:24










  • $begingroup$
    Well that's really all that was in the question. Basically it said the expression for the composition of f(x) and g(x) is that, and it asked to find expressions for f(x) and g(x)
    $endgroup$
    – Daniel Amaral
    Apr 7 at 18:25















$begingroup$
$fg$ is the product of $f,g$ or their composition?
$endgroup$
– Shubham Johri
Apr 7 at 18:20




$begingroup$
$fg$ is the product of $f,g$ or their composition?
$endgroup$
– Shubham Johri
Apr 7 at 18:20












$begingroup$
It is their composition. Also, it is 2 to the power of (x+5). Sorry I am new here I wasn't really sure how to make it like that.
$endgroup$
– Daniel Amaral
Apr 7 at 18:21




$begingroup$
It is their composition. Also, it is 2 to the power of (x+5). Sorry I am new here I wasn't really sure how to make it like that.
$endgroup$
– Daniel Amaral
Apr 7 at 18:21




4




4




$begingroup$
You should probably add more context, this way it is not clear for what do you want this, for example $g(x)=x$ and $f(x)=2^x+5$ would satisfy your requirements, but I doubt it is of any use.
$endgroup$
– Sil
Apr 7 at 18:22





$begingroup$
You should probably add more context, this way it is not clear for what do you want this, for example $g(x)=x$ and $f(x)=2^x+5$ would satisfy your requirements, but I doubt it is of any use.
$endgroup$
– Sil
Apr 7 at 18:22













$begingroup$
In other words, there are infinitely many solutions to your problem. Consider $f(x)=2^nx+5,g(x)=x/n$.
$endgroup$
– Shubham Johri
Apr 7 at 18:24




$begingroup$
In other words, there are infinitely many solutions to your problem. Consider $f(x)=2^nx+5,g(x)=x/n$.
$endgroup$
– Shubham Johri
Apr 7 at 18:24












$begingroup$
Well that's really all that was in the question. Basically it said the expression for the composition of f(x) and g(x) is that, and it asked to find expressions for f(x) and g(x)
$endgroup$
– Daniel Amaral
Apr 7 at 18:25




$begingroup$
Well that's really all that was in the question. Basically it said the expression for the composition of f(x) and g(x) is that, and it asked to find expressions for f(x) and g(x)
$endgroup$
– Daniel Amaral
Apr 7 at 18:25










2 Answers
2






active

oldest

votes


















8












$begingroup$

Without more context, there are, of course, many solutions. For example, a rather trivial one would be $f(x)=x, g(x)=2^x+5$ (or switch the two around) or $f(x)=2^x$ and $g(x)=x+5$. More examples include $f(x)=2^x+t, g(x)=x+5-t$ for any fixed $t$, $g(x)=2^2x+10, f(x)=sqrtx$, etc.






share|cite|improve this answer









$endgroup$




















    5












    $begingroup$

    While there are infinitely-many functions $f,g$ that would do the trick, this is probably intended to give you practice choosing fairly basic (even fundamental) examples, but without just choosing one of them to be the identity function. Clearly, we'll need one of our functions to be $2^textsomething involving x$ in order for that to happen. Ideally, we'd like it to be simply $2^x.$ But which one should it be? Well, it turns out not to matter.



    If we make $f(x)=2^x,$ then $fbigl(g(x)bigr)=2^g(x),$ so we'd need $g(x)=x+5.$



    On the other hand, if we made $g(x)=2^x,$ then we'd have $fbigl(g(x)bigr)=fleft(2^xright),$ but what can we do to $2^x$ to turn it into $2^x+5$? Well, remember your exponent rules: $2^x+5=2^xcdot 2^5=2^xcdot 32.$ Thus, we need $f(x)=32x.$






    share|cite|improve this answer









    $endgroup$



















      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      8












      $begingroup$

      Without more context, there are, of course, many solutions. For example, a rather trivial one would be $f(x)=x, g(x)=2^x+5$ (or switch the two around) or $f(x)=2^x$ and $g(x)=x+5$. More examples include $f(x)=2^x+t, g(x)=x+5-t$ for any fixed $t$, $g(x)=2^2x+10, f(x)=sqrtx$, etc.






      share|cite|improve this answer









      $endgroup$

















        8












        $begingroup$

        Without more context, there are, of course, many solutions. For example, a rather trivial one would be $f(x)=x, g(x)=2^x+5$ (or switch the two around) or $f(x)=2^x$ and $g(x)=x+5$. More examples include $f(x)=2^x+t, g(x)=x+5-t$ for any fixed $t$, $g(x)=2^2x+10, f(x)=sqrtx$, etc.






        share|cite|improve this answer









        $endgroup$















          8












          8








          8





          $begingroup$

          Without more context, there are, of course, many solutions. For example, a rather trivial one would be $f(x)=x, g(x)=2^x+5$ (or switch the two around) or $f(x)=2^x$ and $g(x)=x+5$. More examples include $f(x)=2^x+t, g(x)=x+5-t$ for any fixed $t$, $g(x)=2^2x+10, f(x)=sqrtx$, etc.






          share|cite|improve this answer









          $endgroup$



          Without more context, there are, of course, many solutions. For example, a rather trivial one would be $f(x)=x, g(x)=2^x+5$ (or switch the two around) or $f(x)=2^x$ and $g(x)=x+5$. More examples include $f(x)=2^x+t, g(x)=x+5-t$ for any fixed $t$, $g(x)=2^2x+10, f(x)=sqrtx$, etc.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Apr 7 at 18:27









          Yuval GatYuval Gat

          9641213




          9641213





















              5












              $begingroup$

              While there are infinitely-many functions $f,g$ that would do the trick, this is probably intended to give you practice choosing fairly basic (even fundamental) examples, but without just choosing one of them to be the identity function. Clearly, we'll need one of our functions to be $2^textsomething involving x$ in order for that to happen. Ideally, we'd like it to be simply $2^x.$ But which one should it be? Well, it turns out not to matter.



              If we make $f(x)=2^x,$ then $fbigl(g(x)bigr)=2^g(x),$ so we'd need $g(x)=x+5.$



              On the other hand, if we made $g(x)=2^x,$ then we'd have $fbigl(g(x)bigr)=fleft(2^xright),$ but what can we do to $2^x$ to turn it into $2^x+5$? Well, remember your exponent rules: $2^x+5=2^xcdot 2^5=2^xcdot 32.$ Thus, we need $f(x)=32x.$






              share|cite|improve this answer









              $endgroup$

















                5












                $begingroup$

                While there are infinitely-many functions $f,g$ that would do the trick, this is probably intended to give you practice choosing fairly basic (even fundamental) examples, but without just choosing one of them to be the identity function. Clearly, we'll need one of our functions to be $2^textsomething involving x$ in order for that to happen. Ideally, we'd like it to be simply $2^x.$ But which one should it be? Well, it turns out not to matter.



                If we make $f(x)=2^x,$ then $fbigl(g(x)bigr)=2^g(x),$ so we'd need $g(x)=x+5.$



                On the other hand, if we made $g(x)=2^x,$ then we'd have $fbigl(g(x)bigr)=fleft(2^xright),$ but what can we do to $2^x$ to turn it into $2^x+5$? Well, remember your exponent rules: $2^x+5=2^xcdot 2^5=2^xcdot 32.$ Thus, we need $f(x)=32x.$






                share|cite|improve this answer









                $endgroup$















                  5












                  5








                  5





                  $begingroup$

                  While there are infinitely-many functions $f,g$ that would do the trick, this is probably intended to give you practice choosing fairly basic (even fundamental) examples, but without just choosing one of them to be the identity function. Clearly, we'll need one of our functions to be $2^textsomething involving x$ in order for that to happen. Ideally, we'd like it to be simply $2^x.$ But which one should it be? Well, it turns out not to matter.



                  If we make $f(x)=2^x,$ then $fbigl(g(x)bigr)=2^g(x),$ so we'd need $g(x)=x+5.$



                  On the other hand, if we made $g(x)=2^x,$ then we'd have $fbigl(g(x)bigr)=fleft(2^xright),$ but what can we do to $2^x$ to turn it into $2^x+5$? Well, remember your exponent rules: $2^x+5=2^xcdot 2^5=2^xcdot 32.$ Thus, we need $f(x)=32x.$






                  share|cite|improve this answer









                  $endgroup$



                  While there are infinitely-many functions $f,g$ that would do the trick, this is probably intended to give you practice choosing fairly basic (even fundamental) examples, but without just choosing one of them to be the identity function. Clearly, we'll need one of our functions to be $2^textsomething involving x$ in order for that to happen. Ideally, we'd like it to be simply $2^x.$ But which one should it be? Well, it turns out not to matter.



                  If we make $f(x)=2^x,$ then $fbigl(g(x)bigr)=2^g(x),$ so we'd need $g(x)=x+5.$



                  On the other hand, if we made $g(x)=2^x,$ then we'd have $fbigl(g(x)bigr)=fleft(2^xright),$ but what can we do to $2^x$ to turn it into $2^x+5$? Well, remember your exponent rules: $2^x+5=2^xcdot 2^5=2^xcdot 32.$ Thus, we need $f(x)=32x.$







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Apr 7 at 18:34









                  Cameron BuieCameron Buie

                  86.8k773161




                  86.8k773161













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