Question

select the correct answer from each drop - down menu.
sofia used these steps to find the inverse of function f.

step number	function	step description
step 2	$y = \frac{3x + 4}{8}$	change $f(x)$ to $y$
step 3	$x = \frac{3y + 4}{8}$	switch $x$ and $y$
step 4	$8x = 3y + 4$	multiply each side by 8
step 5	$8x - 4 = 3y$	subtract 4 from each side
step 6	$24x - 12 = y$	multiply each side by 3
step 7	$24x - 12 = f^{-1}(x)$	replace $y$ with $f^{-1}(x)$

use this information to complete the statement.
sofia made a mistake in step \\(\square\\). she should have \\(\square\\).

Explanation:

Step1: Analyze Step 6

From Step 5, we have \(8x - 4 = 3y\). To solve for \(y\), we should divide both sides by 3, not multiply by 3.

Step2: Correct Operation for Step 6

Dividing \(8x - 4 = 3y\) by 3 gives \(y=\frac{8x - 4}{3}\) (or equivalently \(y = \frac{8}{3}x-\frac{4}{3}\)), not multiplying by 3. So the mistake is in Step 6, and the correct operation is to divide each side by 3 (or perform the correct isolation of \(y\) by dividing instead of multiplying).

Answer:

Sofia made a mistake in step 6. She should have divided each side by 3 (or solved \(8x - 4 = 3y\) for \(y\) by dividing both sides by 3, resulting in \(y=\frac{8x - 4}{3}\) or equivalent).