Q 43. - Precalculus Enhanced with Graphing Utilities

Question

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

The inverse of the function in red color is shown below.

Step 1. Given information.

Given a graph of a function f along with $y=x$ as shwon below.

Step 2. Find the coordinates of f - 1 and plot it.

Note that if $\left(x,y\right)$ lies on f, then $\left(y,x\right)$ lies on $f^{-1}$.

Since the points $\left(1,2\right),\left(0,1\right),\left(-1,0\right),\left(-2,-2\right)$ are on the graph f, the points $\left(2,1\right),\left(1,0\right),\left(0,-1\right),\left(-2,-2\right)$ must be on the graph of $f^{-1}$.

Keeping in mind that the graph of $f^{-1}$ is the reflection about the

line $y=x$ of the graph of f, draw inverse of the function in red color as shown below.

Blue color denotes the function f.