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

Question

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: \[ f^{-1}(x) = \frac{2}{5}x - 4 \]