Question

Find the inverse function in slope-intercept form (mx+b):
f, of, x, equals, start fraction, 5, divided by, 2, end fraction, x, plus, 10
f(x)=
2
5
​
x+10

Answer 1

To find the inverse function of \( f(x) = \frac{5}{2}x + 10 \), we can follow these steps:

1. Replace \( f(x) \) with \( y \):
\[
y = \frac{5}{2}x + 10
\]

2. Swap \( x \) and \( y \) to find the inverse:
\[
x = \frac{5}{2}y + 10
\]

3. Solve for \( y \):
- First, subtract 10 from both sides:
\[
x - 10 = \frac{5}{2}y
\]
- Now, multiply both sides by \( \frac{2}{5} \) to isolate \( y \):
\[
y = \frac{2}{5}(x - 10)
\]
- Expand the right side:
\[
y = \frac{2}{5}x - 4
\]

4. So the inverse function is:
\[
f^{-1}(x) = \frac{2}{5}x - 4
\]

In slope-intercept form (mx + b), the inverse function is:
\[
f^{-1}(x) = \frac{2}{5}x - 4
\]