Chapter 7, Problem 3PT

.

To determine

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

Answer to Problem 3PT

Yes

Explanation of Solution

Given Information:

The functions are :

  $\begin{array}{l}f(x)=x+7\\ g(x)=x-7\end{array}$

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:

  $\begin{array}{l}Given\\ f(x)=x+7\\ g(x)=x-7\\ Check:\\ \left[f\circ g\right](x)=f\left[g(x)\right]=f\left(x-7\right)=(x-7)+7=x\\ \left[g\circ f\right](x)=g\left[f(x)\right]=g\left(x+7\right)=(x+7)-7=x\\ Hence,\text{f and g are inverses}\text{.}\end{array}$