Inverse of $$$y = \ln\left(x\right) - 1$$$

Find the inverse of the function $$$y = \ln\left(x\right) - 1$$$.

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: $$$y = \ln\left(x\right) - 1$$$ becomes $$$x = \ln\left(y\right) - 1$$$.

Now, solve the equation $$$x = \ln\left(y\right) - 1$$$ for $$$y$$$.

$$$y = e^{x + 1}$$$

$$$y = e^{x + 1}$$$A

Graph: see the graphing calculator.