Question

1. find the inverse of

$f(x) = \frac{1}{3}x - 2$
rewrite as y =
switch x and y
solve for y

Explanation:

Step1: Rewrite function as $y$

$y = \frac{1}{3}x - 2$

Step2: Switch $x$ and $y$

$x = \frac{1}{3}y - 2$

Step3: Isolate the $y$-term

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

Step4: Solve for $y$

$y = 3(x + 2) = 3x + 6$

Answer:

$f^{-1}(x) = 3x + 6$