Inverse of $y = e^{x}$

To find the inverse function, swap $x$ and $y$, and solve the resulting equation for $y$.

This means that the inverse is the reflection of the function over the line $y = x$.

If the initial function is not one-to-one, then there will be more than one inverse.

So, swap the variables: $y = e^{x}$ becomes $x = e^{y}$.

Now, solve the equation $x = e^{y}$ for $y$.

$y = \ln\left(x\right)$

$y = \ln\left(x\right)$A

Graph: see the graphing calculator.