Chapter 4, Problem 62SGR

To determine

To find the inverse of the function $f\left(x\right)=2-3x$ .

Answer to Problem 62SGR

  $f^{-1}\left(x\right)=\frac{1}{3}\left(2-x\right)$

Explanation of Solution

Given:

  $f\left(x\right)=2-3x$

Calculation:

Let us consider,

  $y=2-3x$

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

  $\begin{array}{l}x=2-3y\\ \Rightarrow 3y=2-x\\ \Rightarrow y=\frac{1}{3}\left(2-x\right)\\ \therefore f^{-1}\left(x\right)=\frac{1}{3}\left(2-x\right)\end{array}$