Chapter 3, Problem 20TP

Solution

Whether the given functions are inverse of each other or not.

  $\text{No}$

Given information:

The graph of functions f and g

  

Concept used:

• The graph of the function $y=f\left(x\right)$ and its inverse $f^{-1}\left(x\right)$ are symmetric to the line $y=x$ .
• For any point $\left(a,b\right)$ on the graph of $f\left(x\right)$ , the corresponding point on the graph of inverse function $f^{-1}\left(x\right)$ is $\left(b,a\right)$ .
• If a function is one-to-one, then it has an inverse.

Calculation:

Recall that the graph of the function $y=f\left(x\right)$ and its inverse $f^{-1}\left(x\right)$ are symmetric to the line $y=x$ .

If there is a point $\left(a,b\right)$ on the graph of $f\left(x\right)$ , the corresponding point on the graph of inverse function $f^{-1}\left(x\right)$ is given by $\left(b,a\right)$ .

From the given graph note that f passes through the point $\left(2,3\right)$ but the graph of g does not pass from the corresponding point $\left(3,2\right)$ .

Thus, the given functions are not inverse functions.