Question

find the inverse function in slope-intercept form (mx+b):
$f(x) = \frac{4}{3}x + 8$

Explanation:

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

$y = \frac{4}{3}x + 8$

Step2: Swap $x$ and $y$

$x = \frac{4}{3}y + 8$

Step3: Isolate the $y$-term

$x - 8 = \frac{4}{3}y$

Step4: Solve for $y$

$y = \frac{3}{4}(x - 8) = \frac{3}{4}x - 6$

Answer:

$f^{-1}(x) = \frac{3}{4}x - 6$