Find the inverse function in slope-intercept form (mx+b):

Question

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:

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