Question

what is the inverse of the function $f(x) = \frac{1}{4}x - 12$?
\bigcirc $h(x) = 48x - 4$
\bigcirc $h(x) = 48x + 4$
\bigcirc $h(x) = 4x - 48$
\bigcirc $h(x) = 4x + 48$

Explanation:

Step1: Replace \( f(x) \) with \( y \)

We start with the function \( f(x)=\frac{1}{4}x - 12 \). Replace \( f(x) \) with \( y \), so we have \( y=\frac{1}{4}x - 12 \).

Step2: Swap \( x \) and \( y \)

To find the inverse, we swap the roles of \( x \) and \( y \). This gives us \( x=\frac{1}{4}y - 12 \).

Step3: Solve for \( y \)

First, add 12 to both sides of the equation: \( x + 12=\frac{1}{4}y \).
Then, multiply both sides by 4 to isolate \( y \): \( y = 4(x + 12) \).
Simplify the right - hand side: \( y=4x + 48 \).

Answer:

\( h(x)=4x + 48 \) (the fourth option: \( h(x) = 4x + 48 \))