Question

find the inverse function in slope-intercept form (mx+b):
$f(x) = -dfrac{3}{4}x - 15$

Explanation:

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

\( y = -\frac{3}{4}x - 15 \)

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

\( x = -\frac{3}{4}y - 15 \)

Step3: Solve for \( y \)

First, add 15 to both sides: \( x + 15 = -\frac{3}{4}y \)
Then, multiply both sides by \( -\frac{4}{3} \): \( y = -\frac{4}{3}(x + 15) \)
Expand the right side: \( y = -\frac{4}{3}x - 20 \)

Answer:

The inverse function in slope - intercept form is \( f^{-1}(x)=-\frac{4}{3}x - 20 \)