Chapter 4, Problem 52SGR

To determine

To find the inverse of the function $f\left(x\right)=\frac{1}{4}x-7$ .

Answer to Problem 52SGR

  $f^{-1}\left(x\right)=4x+28$

Explanation of Solution

Given:

  $f\left(x\right)=\frac{1}{4}x-7$

Calculation:

Let us consider,

  $y=\frac{1}{4}x-7$

To find inverse function, replace $y$ by $x$ and then solve for $y$ in terms of $x$ . That is,

  $\begin{array}{l}x=\frac{1}{4}y-7\\ \Rightarrow \frac{1}{4}y=x+7\\ \Rightarrow y=4\left(x+7\right)\\ \Rightarrow y=4x+28\\ \therefore f^{-1}\left(x\right)=4x+28\end{array}$