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

Explanation:

Step1: Replace f(x) with y

We start by writing the function as ( y = \frac{1}{4}x - 12 ).

Step2: Swap x and y

Interchange the roles of x and y to get ( x = \frac{1}{4}y - 12 ).

Step3: Solve for y

First, add 12 to both sides: ( x + 12 = \frac{1}{4}y ). Then, multiply both sides by 4 to isolate y: ( y = 4(x + 12) = 4x + 48 ). So the inverse function ( h(x) = 4x + 48 ).

Answer:

D. ( h(x) = 4x + 48 ) (assuming the options are labeled A to D in order, with the last option being D)