Chapter 6.2, Problem 4CYU

To determine

To find: The inverse of the given function and the graph of given function and its inverse.

Answer to Problem 4CYU

The inverse of the given function is $y=\frac{x+6}{4}$ .

Explanation of Solution

Given:

The given function is $g\left(x\right)=4x-6$

Calculation:

The inverse of a function is obtained by interchanging the variables and then finding the new value of the function.

Interchange the variables of the function,

  $\begin{array}{l}y=4x-6\\ x=4y-6\end{array}$

Solve for y .

  $y=\frac{x+6}{4}$

Therefore, the inverse of the given function is $y=\frac{x+6}{4}$ .

The plot of $g\left(x\right)=4x-6$ is :

  

The plot of the inverse $y=\frac{x+6}{4}$ is