Question

Find the inverse function in slope-intercept form (mx+b):
f, of, x, equals, minus, 2, x, minus, 10
f(x)=
−2x−10

Answer 1

To find the inverse function of \( f(x) = -2x - 10 \), we follow these steps:

1. **Replace \( f(x) \) with \( y \)**:
\[
y = -2x - 10
\]

2. **Swap \( x \) and \( y \)** to find the inverse:
\[
x = -2y - 10
\]

3. **Solve for \( y \)**:
- First, isolate the term with \( y \):
\[
x + 10 = -2y
\]
- Next, divide by -2:
\[
y = \frac{-1}{2}(x + 10)
\]
- This simplifies to:
\[
y = -\frac{1}{2}x - 5
\]

4. **Write the inverse function**:
\[
f^{-1}(x) = -\frac{1}{2}x - 5
\]

The inverse function in slope-intercept form is:
\[
f^{-1}(x) = -\frac{1}{2}x - 5
\]