Chapter 4, Problem 64SGR

To determine

To find the inverse of the function $f\left(x\right)=2+\frac{3x}{5}$ .

Answer to Problem 64SGR

  $f^{-1}\left(x\right)=\frac{5}{3}\left(x-2\right)$

Explanation of Solution

Given:

  $f\left(x\right)=2+\frac{3x}{5}$

Calculation:

Let us consider,

  $y=2+\frac{3x}{5}$

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

  $\begin{array}{l}x=2+\frac{3y}{5}\\ \Rightarrow \frac{3y}{5}=x-2\\ \Rightarrow y=\frac{5}{3}\left(x-2\right)\\ \therefore f^{-1}\left(x\right)=\frac{5}{3}\left(x-2\right)\end{array}$