Question

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

f, to the power minus 1 , left parenthesis, x, right parenthesis, equalsf
−1
(x)=

Answer 1

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

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

2. **Switch \( x \) and \( y \)**:
\[
x = -2y + 2
\]

3. **Solve for \( y \)**:
\[
x - 2 = -2y
\]
\[
-2y = x - 2
\]
\[
y = -\frac{1}{2}(x - 2)
\]
\[
y = -\frac{1}{2}x + 1
\]

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

Thus, the inverse function in slope-intercept form (mx + b) is:

\[
f^{-1}(x) = -\frac{1}{2}x + 1
\]