Question

Talib is trying to find the inverse of the function to the right. His work appears beneath it. Is his work correct? Explain your answer.

Answer 1

Given the function
$f(x)=-8x+4$

The inverse of the function is calculated by changing f(x) to y and making x the subject of the formula as follows:
$y=-8x+4 \\ \\ y-4=-8x \\ \\ x= \frac{y-4}{-8}$

We now change back the variables to get the function in the form of inverse function as follows:
$f^{-1}(x)=\frac{x-4}{-8}$

Comparing this with Talib's work, we can see that he is correct except for the last line where he did not change the variable y back to x.

Therefore, the last line of his work made his inverse not to be correct.

Answer 2

The sample response on e2020 is: His work is not correct. You first must switch x and y and then solve for y.