Question

find the inverse function in slope-intercept form (mx+b):
$f(x) = -\frac{1}{3}x + 15$

Explanation:

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

\( y = -\frac{1}{3}x + 15 \)

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

\( x = -\frac{1}{3}y + 15 \)

Step3: Solve for \( y \)

First, subtract 15 from both sides: \( x - 15 = -\frac{1}{3}y \)
Then, multiply both sides by -3: \( y = -3(x - 15) \)
Simplify: \( y = -3x + 45 \)

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

\( f^{-1}(x) = -3x + 45 \)

Answer:

\( f^{-1}(x) = -3x + 45 \)