Q 8. - Precalculus Enhanced with Graphing Utilities

Question

If $f^{-1}$ denotes the inverse of a function $f$, then the graphs of $f$ and $f^{-1}$ are symmetric with respect to the line $\dots \dots$

Step-by-Step Solution

Answer

If $f^{-1}$ denotes the inverse of a function $f$, then the graph of $f$ and $f^{-1}$ are symmetric with respect to the line $y=x$.

Step 1. Definition

The inverse function is a function obtained by reversing the given function. The domain and range of the given function are changed as the range and domain .

Step 2. Explanation

If $\left(a,b\right)$ is a point on the graph of a function $f$ then $\left(b,a\right)$ is a point on the graph of its inverse.

Furthermore, the two graphs will be symmetric about the line $y=x$ have symmetry when graphed on the same set of axes.