Q 45. - Precalculus Enhanced with Graphing Utilities

Question

In Problem, the graph of a one-to-one function $f$ is given. Draw the graph of the inverse function $f^{-1}$. For convenience (and as a hint), the graph of $y = x$ is also given.

Step-by-Step Solution

Answer

Step 1: Given information

Graph of $f$ is given as follows:

Step 2. Graph of f - 1

We know that the graph of a function f and the graph of its inverse is symmetric with respect to the line y = x

For every point (x, y) on the graph of f(x), there will be a symmetric point (y, x) which will be on the graph of $f^{-1}\left(x\right)$.

Points on the given graph of f(x) are $(-1,-1),(0,0),(2,1)$.

So, the corresponding points on the graph of $f^{-1}\left(x\right)$ are $(-1,-1),(0,0),(1,2)$.