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

Question

f, of, x, equals, minus, one half, x, plus, 8
f(x)=
−
2
1
​
x+8

Answer 1

To find the inverse function of \( f(x) = -\frac{1}{2}x + 8 \), we need to follow these steps:

1. Replace \( f(x) \) with \( y \): \[ y = -\frac{1}{2}x + 8 \]

2. Solve for \( x \) in terms of \( y \): \[ y - 8 = -\frac{1}{2}x \] Multiply both sides by -2 to isolate \( x \): \[ -2(y - 8) = x \] or, \[ x = -2y + 16 \]

3. Now, swap \( x \) and \( y \): \[ y = -2x + 16 \]

4. Finally, write the inverse function: \[ f^{-1}(x) = -2x + 16 \]

Thus, the inverse function \( f^{-1}(x) \) in slope-intercept form is: \[ f^{-1}(x) = -2x + 16 \]