Chapter 4, Problem 60SGR

To determine

To find the inverse of the function $f\left(x\right)=-5x-\frac{6}{7}$ .

Answer to Problem 60SGR

  $f^{-1}\left(x\right)=-\frac{1}{5}x-\frac{6}{35}$

Explanation of Solution

Given:

  $f\left(x\right)=-5x-\frac{6}{7}$

Calculation:

Let us consider,

  $y=-5x-\frac{6}{7}$

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

  $\begin{array}{l}x=-5y-\frac{6}{7}\\ \Rightarrow -5y=x+\frac{6}{7}\\ \Rightarrow y=-\frac{1}{5}\left(x+\frac{6}{7}\right)\\ \Rightarrow y=-\frac{1}{5}x-\frac{6}{35}\\ \therefore f^{-1}\left(x\right)=-\frac{1}{5}x-\frac{6}{35}\end{array}$