Question

which represents the inverse of the function $f(x) = 4x$?
$h(x) = x + 4$
$h(x) = x - 4$
$h(x) = \frac{3}{4}x$
$h(x) = \frac{1}{4}x$

Explanation:

Step1: Replace f(x) with y

$y = 4x$

Step2: Swap x and y variables

$x = 4y$

Step3: Solve for y

$\frac{x}{4} = y$ or $y = \frac{1}{4}x$

Step4: Rename y as inverse function

$h(x) = \frac{1}{4}x$

Answer:

D. $h(x)=\frac{1}{4}x$