Chapter 6, Problem 4PT

To determine

Whether the given functions are inverses or not.State Yes or No.

Answer to Problem 4PT

No

Explanation of Solution

Given Information:

The functions are :

  $\begin{array}{l}f(x)=\frac{x-2}{3}\\ g(x)=3x-2\end{array}$

Concept Used:

Two functions f and g are inverse of each other if and only if :

  $\begin{array}{l}\left[f\circ g\right](x)=x\\ and\\ \left[g\circ f\right](x)=x\end{array}$

Calculation:

  $\begin{array}{l}Given\\ f(x)=\frac{x-2}{3}\\ g(x)=3x-2\\ Check:\\ \left[g\circ f\right](x)=g\left[f(x)\right]=g\left(\frac{x-2}{3}\right)=3\left(\frac{x-2}{3}\right)-2=x-2-2\ne x\\ Hence,\text{f and g are not inverses}\text{.}\end{array}$