# What is the graph of the inverse function?

Nov 24, 2015

A reflection over the line $y = x$.

#### Explanation:

Inverse graphs have swapped domains and ranges. That is, the domain of the original function is the range of its inverse, and its range is the inverse's domain. Along with this, the point $\left(- 1 , 6\right)$ in the original function will be represented by the point $\left(6 , - 1\right)$ in the inverse function.

Inverse functions' graphs are reflections over the line $y = x$.

The inverse function of $f \left(x\right)$ is written as ${f}^{-} 1 \left(x\right)$.

$\left\{\begin{matrix}f \left({f}^{-} 1 \left(x\right)\right) = x \\ {f}^{-} 1 \left(f \left(x\right)\right) = x\end{matrix}\right.$

If this is $f \left(x\right)$: graph{lnx+2 [-10, 10, -5, 5]}

This is ${f}^{-} 1 \left(x\right)$: graph{e^(x-2) [-9.79, 10.21, -3.4, 6.6]}