Chapter 4, Problem 57SGR

To determine

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

Answer to Problem 57SGR

  $f^{-1}\left(x\right)=\frac{1}{4}\left(x+7\right)$

Explanation of Solution

Given:

  $f\left(x\right)=4x-7$

Calculation:

Let us consider,

  $y=4x-7$

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

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