Question

find the invers function in slope intercept form mx+b
f(x)=5/2x-5

f^-1 (x)=

Answer 1

To find the inverse of the function \( f(x) = \frac{5}{2}x - 5 \), we need to follow these steps:

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

2. **Swap \( x \) and \( y \)**:
\[
x = \frac{5}{2}y - 5
\]

3. **Solve for \( y \)**:
\[
x + 5 = \frac{5}{2}y
\]
\[
y = \frac{2}{5}(x + 5)
\]

Now, distribute the \( \frac{2}{5} \):
\[
y = \frac{2}{5}x + \frac{10}{5}
\]
\[
y = \frac{2}{5}x + 2
\]

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

So the inverse function in slope-intercept form is:
\[
f^{-1}(x) = \frac{2}{5}x + 2
\]