Question

find the inverse function of the function $f(x)=\frac{1}{5}x - 5$.
answer
$\bigcirc \\ f^{-1}(x)=\frac{1}{5}x + 25$
$\bigcirc \\ f^{-1}(x)=5x + 25$
$\bigcirc \\ f^{-1}(x)=\frac{1}{5}x + 5$
$\bigcirc \\ f^{-1}(x)=5x + 5$

Explanation:

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

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

Step2: Swap $x$ and $y$

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

Step3: Isolate the term with $y$

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

Step4: Solve for $y$

$y = 5(x + 5) = 5x + 25$

Step5: Replace $y$ with $f^{-1}(x)$

$f^{-1}(x) = 5x + 25$

Answer:

$f^{-1}(x) = 5x + 25$