Question

1. find the inverse of each function.

a. $y = \frac{x - 6}{4}$

Explanation:

Step1: Swap x and y

To find the inverse of a function, we first swap the roles of \( x \) and \( y \) in the equation \( y = \frac{x - 6}{4} \). So we get \( x=\frac{y - 6}{4} \).

Step2: Solve for y

Multiply both sides of the equation \( x=\frac{y - 6}{4} \) by 4 to get rid of the denominator on the right side. We have \( 4x=y - 6 \). Then, add 6 to both sides of the equation to solve for \( y \). So \( y = 4x+6 \).

Answer:

The inverse function is \( y = 4x + 6 \) (or we can write it as \( f^{-1}(x)=4x + 6 \))