Chapter 6.2, Problem 3AGP

To determine

To Find :

Whether the given functions are inverses or not.

Answer to Problem 3AGP

No

Explanation of Solution

Given :

The functions are :

  $f(x)=3x-3,g(x)=\frac{1}{3}x+4$

Concept Used :

Two functions f and g are inverse functions if and only if both of their compositions are the identity function.

f(x) and g(x) are inverses if and only if $\left[f\circ g\right](x)=x\text{ and }\left[g\circ f\right](x)=x$

Calculation:

  $\begin{array}{l}Given\\ f(x)=3x-3,g(x)=\frac{1}{3}x+4\\ \left[f\circ g\right](x)=f\left[g(x)\right]=f\left(\frac{1}{3}x+4\right)=3\left(\frac{1}{3}x+4\right)-3=x+12-3\ne x\\ \text{For two functions f and g to be inverses , their composition should be identity function,}\\ \text{which is not true here}\text{.}\\ \text{So, given functions are not inverses}\text{.}\end{array}$