Chapter 1, Problem 49RE

Solution

The graph of the inverse relation of $y=f\left(x\right)$ .

The graph of $y=f\left(-x\right)$ is the reflection of $y=f\left(x\right)$ across horizontal axis.

Given:

The graph of $y=f\left(x\right)$ is

  

Concept Used:

The graph inverse relation of $y=f\left(x\right)$ is the reflection across line $x=y$ and inverse of function is given by solution of y that is obtained by swapping of x and y in original function.

And, in case the original function is not one to one there is more than one inverse.

Calculation:

The graph of $y=f^{-1}\left(x\right)$ is the reflection of $y=f\left(x\right)$ across line $x=y$ . The graph reflected from original $y=f\left(x\right)$ across line $x=y$ shown below,

  

Hence, the desired graph of inverse relation is: