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

Question

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