Solving inverse function

Hello I am having difficulty solving this question. Any help would be greatly appreciated.
$\displaystyle g(x)=3+x+e^x$
The e is the mathematical constant not a variable

find $\displaystyle g^{-1}(4)$

So I must find a value of x where g(x)=4

this is my attempt:
$\displaystyle 4=3+x+e^x$
$\displaystyle 1=x+e^x$
$\displaystyle 1-x=e^x$
I know that ln(e^x)=x so I thought of doing that
ln(1-x)=x
But I don't know what to do after that. Thanks for the assistance.

Quote:

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Originally Posted by iamanoobatmath

Hello I am having difficulty solving this question. Any help would be greatly appreciated.
$\displaystyle g(x)=3+x+e^x$
The e is the mathematical constant not a variable

find $\displaystyle g^{-1}(4)$

So I must find a value of x where g(x)=4

this is my attempt:
$\displaystyle 4=3+x+e^x$
$\displaystyle 1=x+e^x$
$\displaystyle 1-x=e^x$
I know that ln(e^x)=x so I thought of doing that
ln(1-x)=x
But I don't know what to do after that. Thanks for the assistance.

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At this stage, I can only complete it by observation:

If $\displaystyle x=0$, then $\displaystyle 1-0=e^0\implies 1=1$

So $\displaystyle g^{-1}(4)=0$

Quote:

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Originally Posted by Chris L T521

At this stage, I can only complete it by observation:

If $\displaystyle x=0$, then $\displaystyle 1-0=e^0\implies 1=1$

So $\displaystyle g^{-1}(4)=0$

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Undoubtedly a solution by inspection was intended.