Question

1. find the inverse of

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

Explanation:

Step1: Rewrite $f(x)$ as $y$

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

Step2: Swap $x$ and $y$

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

Step3: Multiply both sides by 3

$3x = -(2y+1)$

Step4: Remove parentheses

$3x = -2y -1$

Step5: Isolate the $y$-term

$2y = -3x -1$

Step6: Solve for $y$

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

Answer:

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