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

To find the inverse of a function, we make the independent variable the subject of the formula.

Thus, the inverse of the given function is evaluated as follows.
$f(x)=-8x+4 \\ y=-8x+4 \\ -8x=y-4 \\ x= \frac{y-4}{-8} \\ f^{-1}(x)=\frac{x-4}{-8}$

From the work show, it can be seen that Talib's work is correct.

Answer 2

For this case what we are going to do is describe the work part by part:

1) Talib made the correct variable change in the first step.

2) Talib made a correct clearance in the second step by passing the number 4 subtracting.

3) Taliz made a correct clearance in the third step by passing the number -8 dividing.

4) Taliz made an incorrect variable change in the last step.

The correct variable change is:

$f(x)^{-1}=\frac{x-4}{-8}$

Answer:

Error in the last step, the correct solution is:

$f(x)^{-1}=\frac{x-4}{-8}$