Chapter EP, Problem 7.2.6EP

To determine

To calculate: The inverse of the functions $y=-5x-6$ . Also graph the function and its inverse.

Answer to Problem 7.2.6EP

The inverse of the function $y=-5x-6$ is $f^{-1}\left(x\right)=\frac{-x-6}{5}$ .

The red line depicts the function $y=-5x-6$ and blue line depicts its inverse $f^{-1}\left(x\right)=\frac{-x-6}{5}$ .

Explanation of Solution

Given information:

The functions $y=-5x-6$ .

Formula used:

If two functions f and $f^{-1}$ are said to be inverse functions then $f\left(a\right)=b$ if and only if $f^{-1}\left(b\right)=a$ .

Calculation:

Consider the functions $y=-5x-6$ .

Let $f\left(x\right)=y$ .

Interchange the position of x and y ,

  $x=-5y-6$

Evaluate the above equation for y ,

  $\begin{array}{c}x=-5y-6\\ 5y=-x-6\\ y=\frac{-x-6}{5}\end{array}$

Replace yby $f^{-1}\left(x\right)$ ,

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

Graph of the function $y=-5x-6$ and its inverse $f^{-1}\left(x\right)=\frac{-x-6}{5}$ is provided below,

The red line depicts the function $y=-5x-6$ and blue line depicts its inverse $f^{-1}\left(x\right)=\frac{-x-6}{5}$ .

Thus, the inverse of the function $y=-5x-6$ is $f^{-1}\left(x\right)=\frac{-x-6}{5}$ .