Chapter 6.2, Problem 6CYU

To determine

To find: If the given pair of functions are inverse of each other.

Answer to Problem 6CYU

Yes. The given pair of functions are inverse of each other.

Explanation of Solution

Given:

The given functions are

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

Calculation:

The inverse of a function is obtained by interchanging the variables and then finding the new value of the function.

Interchange the variables of the function,

  $\begin{array}{l}y=x-7\\ x=y-7\end{array}$

Solve for y .

  $y=x+7$

Therefore, the inverse of the given function $f\left(x\right)=x-7$ is $g\left(x\right)=x+7$ .