Q 46. - 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

Function of $f$ is as follows:

Step 2. Graph of f - 1

As we know that, the graph of an one-to- one function and its inverse function, remains symmetrical with respect to the line y =x, and if a point (a, b) lies on the graph of the function, then the point (b, a) will lie on the graph of its inverse function.

Here, the points $(-2,1),(1,-1)$ lies on the graph of the function, hence the points $(1,-2),(-1,1)$ will lie on the graph of its inverse function. Considering all these points the inverse function graph will be the graph, presented by the dotted lines.

Graph of $f^{-1}$ is as follows: