Question

Sofia used these steps to find the inverse function f. what step did she mess up on and why

Answer 1

Sofia's mistake in finding the inverse function was in step 4. She incorrectly multiplied each side by 3 instead of 8. The correct inverse function is
`\(24x - 12 = f^(-1)(x)\).`

Sofia's mistake in finding the inverse function was in step 4. She incorrectly multiplied each side by 3 instead of 8. The correct inverse function is
`\(24x - 12 = f^(-1)(x)\).`

Sofia made a mistake in step 4. She should have multiplied each side by 8, not 3.

The steps for finding the inverse function of f are as follows:

1. Replace f(x) with y.

2. Switch the x and y variables.

3. Solve for y.

4. Replace y with
`f^(-1)(x).`

Sofia's steps 1-3 are correct. However, in step 4, she multiplied each side by 3 instead of 8. This is incorrect, as it will not produce the correct inverse function.

To correct the mistake, Sofia should multiply each side of step 4 by 8, giving:

8x = 3y + 4

Subtracting 4 from each side and then multiplying each side by 3 gives:

24x - 12 = y

Replacing y with
`f^(-1)(x)` gives the correct inverse function:

24x - 12 =
`f^(-1)(x)`

Therefore, Sofia's mistake was in step 4, where she multiplied each side by 3 instead of 8.