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 1

To find the inverse function, \( f^{-1}(x) \), of the function \( f(x) = -2x + 2 \), we will follow these steps:

1. Start by replacing \( f(x) \) with \( y \):
\[
y = -2x + 2
\]

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

3. Now, solve for \( y \):
- First, subtract 2 from both sides:
\[
x - 2 = -2y
\]
- Next, divide both sides by -2:
\[
y = \frac{-(x - 2)}{2} = -\frac{1}{2}x + 1
\]

4. Replace \( y \) with \( f^{-1}(x) \):
\[
f^{-1}(x) = -\frac{1}{2}x + 1
\]

Thus, the inverse function in slope-intercept form is:
\[
f^{-1}(x) = -\frac{1}{2}x + 1
\]