Chapter 1.6, Problem 17E

To determine

To find: The value of $g^{-1}\left(4\right)$ if $g\left(x\right)=3+x+e^x$.

Answer to Problem 17E

The value of $g^{-1}\left(4\right)=0$.

Explanation of Solution

The given function is $g\left(x\right)=3+x+e^x$.

Notice that the value of $g\left(0\right)=4$ as, $3+0+e^0=4\left[\because e^0=1\right]$.

According to the definition of an inverse function, $f^{-1}\left(y\right)=x$ if and only if $f\left(x\right)=y$ where f is one-to-one.

So, it can be concluded that $g^{-1}\left(4\right)=0$ as $g\left(0\right)=4$.

Therefore, the value of $g^{-1}\left(4\right)=0$.