Chapter 4, Problem 65SGR

To determine

To find the inverse of the function $f\left(x\right)=\frac{-3x-1}{8}$ .

Answer to Problem 65SGR

  $f^{-1}\left(x\right)=-\frac{1}{3}\left(8x+1\right)$

Explanation of Solution

Given:

  $f\left(x\right)=\frac{-3x-1}{8}$

Calculation:

Let us consider,

  $y=\frac{-3x-1}{8}$

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

  $\begin{array}{l}x=\frac{-3y-1}{8}\\ \Rightarrow 8x=-3y-1\\ \Rightarrow 3y=-1-8x\\ \Rightarrow y=\frac{1}{3}\left(-1-8x\right)\\ \Rightarrow y=-\frac{1}{3}\left(8x+1\right)\\ \therefore f^{-1}\left(x\right)=-\frac{1}{3}\left(8x+1\right)\end{array}$