Chapter 4, Problem 66SGR

To determine

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

Answer to Problem 66SGR

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

Explanation of Solution

Given:

  $f\left(x\right)=-\frac{3}{5}x$

Calculation:

Let us consider,

  $y=-\frac{3}{5}x$

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

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