Question

Find the inverse function in slope-intercept form (mx+b):
f, of, x, equals, 5, x, plus, 10
f(x)=
5x+10
Answer

f, to the power minus 1 , left parenthesis, x, right parenthesis, equalsf
−1
(x)

Answer 1

To find the inverse function \( f^{-1}(x) \) of the function \( f(x) = 5x + 10 \), follow these steps:

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

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

3. Solve for \( y \):
- Subtract 10 from both sides:
\[
x - 10 = 5y
\]
- Divide both sides by 5:
\[
y = \frac{x - 10}{5}
\]

4. Write the inverse function:
\[
f^{-1}(x) = \frac{x - 10}{5}
\]

Now, let's express it in slope-intercept form \( mx + b \):
\[
f^{-1}(x) = \frac{1}{5}x - 2
\]

So the final answer is:
\[
f^{-1}(x) = \frac{1}{5}x - 2
\]