Question

find the inverse function in slope-intercept form (mx+b):
$f(x) = -dfrac{2}{3}x - 12$

Explanation:

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

\( y = -\frac{2}{3}x - 12 \)

Step2: Swap \( x \) and \( y \)

\( x = -\frac{2}{3}y - 12 \)

Step3: Solve for \( y \)

First, add 12 to both sides: \( x + 12 = -\frac{2}{3}y \)
Then, multiply both sides by \( -\frac{3}{2} \): \( y = -\frac{3}{2}(x + 12) \)
Expand the right side: \( y = -\frac{3}{2}x - 18 \)

Step4: Replace \( y \) with \( f^{-1}(x) \)

\( f^{-1}(x) = -\frac{3}{2}x - 18 \)

Answer:

\( f^{-1}(x) = -\frac{3}{2}x - 18 \)