Is this an unsolvable function composition problem? Or an absurd?











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I am solving a PDE problem. In a certain point, I achieve the following equality:



$G(3x+1) = y^2 + e^x$



This is,basically, a problem involving function composition. How do I find $G(x)$?



I have faced similar problems needing to find $G(x)$. However, this equality looks like an absurd. I can't see a way to solve this.



Maybe I made a previous mistake before arriving to this line. But I have double checked my previous operations.






functions function-and-relation-composition







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    Is $y$ a function of $x$ ?
    – Yves Daoust
    2 days ago










  • @YvesDaoust, I am not sure how to handle y in this exercise. It could be an independent variable, a dependent variable (f(x)=y) or an unknown constant. I am treating it as an unknown constant.
    – Pedro Delfino
    2 days ago

















up vote
-1
down vote

favorite












I am solving a PDE problem. In a certain point, I achieve the following equality:



$G(3x+1) = y^2 + e^x$



This is,basically, a problem involving function composition. How do I find $G(x)$?



I have faced similar problems needing to find $G(x)$. However, this equality looks like an absurd. I can't see a way to solve this.



Maybe I made a previous mistake before arriving to this line. But I have double checked my previous operations.






functions function-and-relation-composition







share|cite|improve this question


















  • 1




    Is $y$ a function of $x$ ?
    – Yves Daoust
    2 days ago










  • @YvesDaoust, I am not sure how to handle y in this exercise. It could be an independent variable, a dependent variable (f(x)=y) or an unknown constant. I am treating it as an unknown constant.
    – Pedro Delfino
    2 days ago















up vote
-1
down vote

favorite









up vote
-1
down vote

favorite











I am solving a PDE problem. In a certain point, I achieve the following equality:



$G(3x+1) = y^2 + e^x$



This is,basically, a problem involving function composition. How do I find $G(x)$?



I have faced similar problems needing to find $G(x)$. However, this equality looks like an absurd. I can't see a way to solve this.



Maybe I made a previous mistake before arriving to this line. But I have double checked my previous operations.






functions function-and-relation-composition







share|cite|improve this question













I am solving a PDE problem. In a certain point, I achieve the following equality:



$G(3x+1) = y^2 + e^x$



This is,basically, a problem involving function composition. How do I find $G(x)$?



I have faced similar problems needing to find $G(x)$. However, this equality looks like an absurd. I can't see a way to solve this.



Maybe I made a previous mistake before arriving to this line. But I have double checked my previous operations.






functions function-and-relation-composition




functions function-and-relation-composition






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share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked 2 days ago









Pedro Delfino

734




734








  • 1




    Is $y$ a function of $x$ ?
    – Yves Daoust
    2 days ago










  • @YvesDaoust, I am not sure how to handle y in this exercise. It could be an independent variable, a dependent variable (f(x)=y) or an unknown constant. I am treating it as an unknown constant.
    – Pedro Delfino
    2 days ago
















  • 1




    Is $y$ a function of $x$ ?
    – Yves Daoust
    2 days ago










  • @YvesDaoust, I am not sure how to handle y in this exercise. It could be an independent variable, a dependent variable (f(x)=y) or an unknown constant. I am treating it as an unknown constant.
    – Pedro Delfino
    2 days ago










1




1




Is $y$ a function of $x$ ?
– Yves Daoust
2 days ago




Is $y$ a function of $x$ ?
– Yves Daoust
2 days ago












@YvesDaoust, I am not sure how to handle y in this exercise. It could be an independent variable, a dependent variable (f(x)=y) or an unknown constant. I am treating it as an unknown constant.
– Pedro Delfino
2 days ago






@YvesDaoust, I am not sure how to handle y in this exercise. It could be an independent variable, a dependent variable (f(x)=y) or an unknown constant. I am treating it as an unknown constant.
– Pedro Delfino
2 days ago












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You may write
$$G(x)=y^2+e^{(x-1)/3}.$$






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    You may write
    $$G(x)=y^2+e^{(x-1)/3}.$$






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      You may write
      $$G(x)=y^2+e^{(x-1)/3}.$$






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        $$G(x)=y^2+e^{(x-1)/3}.$$






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        You may write
        $$G(x)=y^2+e^{(x-1)/3}.$$







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        answered 2 days ago









        Yves Daoust

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