Question

given: f(x) = \frac{5x + 3}{x - 5}
find the inverse function, f^{-1}(x).
f^{-1}(x) =
question help: video

Explanation:

Step1: Replace f(x) with y

$y = \frac{5x + 3}{x - 5}$

Step2: Swap x and y

$x=\frac{5y + 3}{y - 5}$

Step3: Solve for y

$x(y - 5)=5y+3$
$xy-5x = 5y + 3$
$xy-5y=5x + 3$
$y(x - 5)=5x + 3$
$y=\frac{5x + 3}{x - 5}$

Answer:

$f^{-1}(x)=\frac{5x + 3}{x - 5}$