Question

if $f(x) = 5x$, what is $f^{-1}(x)$?
$\bigcirc$ $f^{-1}(x) = -5x$
$\bigcirc$ $f^{-1}(x) = -\frac{1}{5}x$
$\bigcirc$ $f^{-1}(x) = \frac{1}{5}x$
$\bigcirc$ $f^{-1}(x) = 5x$

Explanation:

Step1: Set $y = f(x)$

$y = 5x$

Step2: Swap $x$ and $y$

$x = 5y$

Step3: Solve for $y$

$y = \frac{1}{5}x$

Step4: Replace $y$ with $f^{-1}(x)$

$f^{-1}(x) = \frac{1}{5}x$

Answer:

C. $f^{-1}(x)=\frac{1}{5}x$