Question

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