Question

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

Explanation:

Step1: Set $y = f(x)$

$y = 4x$

Step2: Swap $x$ and $y$

$x = 4y$

Step3: Solve for $y$

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

Step4: Replace $y$ with $h(x)$

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

Answer:

$\boldsymbol{h(x)=\frac{1}{4}x}$ (the last option)