Question

find the inverse function in slope - intercept form (mx + b):
$f(x)=\frac{5}{3}x - 15$

Explanation:

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

\( y = \frac{5}{3}x - 15 \)

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

\( x = \frac{5}{3}y - 15 \)

Step3: Solve for \( y \). First, add 15 to both sides

\( x + 15 = \frac{5}{3}y \)

Step4: Multiply both sides by \( \frac{3}{5} \) to isolate \( y \)

\( y = \frac{3}{5}(x + 15) \)

Step5: Distribute \( \frac{3}{5} \)

\( y = \frac{3}{5}x + 9 \)

Step6: Replace \( y \) with \( f^{-1}(x) \)

\( f^{-1}(x) = \frac{3}{5}x + 9 \)

Answer:

\( f^{-1}(x) = \frac{3}{5}x + 9 \)