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

Question

f, of, x, equals, minus, 2, x, minus, 10
f(x)=
−2x−10

Answer 1

To find the inverse function of \( f(x) = -2x - 10 \), we follow these steps:

1. Replace \( f(x) \) with \( y \): \[ y = -2x - 10 \]

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

3. Solve for \( y \):

   • First, isolate the term with \( y \): \[ x + 10 = -2y \]
   • Next, divide by -2: \[ y = \frac{-1}{2}(x + 10) \]
   • This simplifies to: \[ y = -\frac{1}{2}x - 5 \]

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

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