Question

Talib is trying to find the inverse of the function to the right, which is F(x) = -8x + 4. His work appears beneath it. Is his work correct? Please explain your answer.

Answer 1

To verify and explain the process of finding the inverse of the function F(x) = -8x + 4, we switch x and y in the original equation and then solve for y to obtain the inverse function, which is F^-1(x) = (x - 4)/-8.

Step-by-step explanation:

The student is asking for verification and explanation on whether their work in finding the inverse function of F(x) = -8x + 4 is correct. To find the inverse of a function, we switch the roles of x and y and then solve for y. Here's how to find the inverse step-by-step:

1. Write the function as y = -8x + 4.
2. Switch the variables x and y to make it x = -8y + 4 to prepare for finding the inverse.
3. Solve for y by first subtracting 4 from both sides to get x - 4 = -8y.
4. Divide both sides by -8 to isolate y, so y = (x - 4)/-8.

This final expression represents the inverse of the original function, which is typically written as F-1(x) = (x - 4)/-8.