To find the inverse of the function [tex]\( f(x) = \frac{1}{4}x - 12 \)[/tex], let's go through the following steps:
1. Rewrite the function in terms of y:
[tex]\[ y = \frac{1}{4}x - 12 \][/tex]
2. Swap x and y to find the inverse function:
[tex]\[ x = \frac{1}{4}y - 12 \][/tex]
3. Solve for y in terms of x:
To solve for [tex]\( y \)[/tex], we need to isolate [tex]\( y \)[/tex] on one side of the equation.
- First, add 12 to both sides:
[tex]\[ x + 12 = \frac{1}{4}y \][/tex]
- Then, multiply both sides by 4 to solve for y:
[tex]\[ 4(x + 12) = y \][/tex]
Simplifying this, we get:
[tex]\[ y = 4x + 48 \][/tex]
Therefore, the inverse function is:
[tex]\[ h(x) = 4x + 48 \][/tex]
Among the provided options, the correct answer is:
[tex]\[ h(x) = 4x + 48 \][/tex]
