Question

Find the inverse function in slope-intercept form (mx+b):
f, of, x, equals, minus, 3, x, minus, 18
f(x)=
−3x−18

Answer 1

To find the inverse function of the given function \( f(x) = -3x - 18 \), we'll follow these steps:

1. **Replace \( f(x) \) with \( y \)**:
\[
y = -3x - 18
\]

2. **Swap \( x \) and \( y \)**:
\[
x = -3y - 18
\]

3. **Solve for \( y \)**:
- First, add 18 to both sides:
\[
x + 18 = -3y
\]
- Next, divide both sides by -3:
\[
y = -\frac{x + 18}{3}
\]
- This simplifies to:
\[
y = -\frac{1}{3}x - 6
\]

4. **Replace \( y \) with \( f^{-1}(x) \)**:
\[
f^{-1}(x) = -\frac{1}{3}x - 6
\]

Thus, the inverse function in slope-intercept form is:
\[
f^{-1}(x) = -\frac{1}{3}x - 6
\]