Question

given: f(x) = \frac{3x + 1}{2x + 5}
find the inverse function, f^{-1}(x).
f^{-1}(x) =
question help: video

Explanation:

Step1: Replace f(x) with y

$y=\frac{3x + 1}{2x+5}$

Step2: Swap x and y

$x=\frac{3y + 1}{2y+5}$

Step3: Solve for y

$x(2y + 5)=3y+1$
$2xy+5x=3y + 1$
$2xy-3y=1 - 5x$
$y(2x - 3)=1-5x$
$y=\frac{1 - 5x}{2x-3}$

Answer:

$f^{-1}(x)=\frac{1 - 5x}{2x-3}$