Question

what is the inverse of the function $f(x) = 4x + 8$?
$h(x) = \frac{1}{4}x - 2$
$h(x) = \frac{1}{4}x + 2$
$h(x) = \frac{1}{2}x - 2$
$h(x) = \frac{1}{2}x + 2$

Explanation:

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

$y = 4x + 8$

Step2: Swap $x$ and $y$

$x = 4y + 8$

Step3: Isolate the term with $y$

$x - 8 = 4y$

Step4: Solve for $y$

$y = \frac{1}{4}x - 2$

Answer:

A. $h(x) = \frac{1}{4}x - 2$