Chapter 6, Problem 8STP

To determine

To Find:

The inverse of $f(x)=x-5$

Answer to Problem 8STP

F

Explanation of Solution

Given Information:

The function is :

  $f(x)=x-5$

Concept Used:

To find the inverse of a function $y=ax+b$ :

• Replace x and y .
• Solve for y .
• The resulting function is the inverse of given function.

Calculation:

  $\begin{array}{l}Given\\ f(x)=x-5\\ \text{To find the inverse :-}\\ \text{Replace f(x) by y :}\\ y=x-5\\ \text{Exchange x and y:}\\ x=y-5\\ Solve\text{ for y :}\\ x+5=y-5+\mathrm{5......}[\text{add 5 each side]}\\ y=x+5\\ So,\\ f^{-1}(x)=x+5\\ Hence,\text{ the correct option is F}\text{.}\end{array}$