Question

Consider the function: f(x) = 4x + 7. Place each step for finding ( f^(-1) (x) ) in the correct order.

A) Rewrite the equation as y = 4x + 7.
B) Interchange x and y to form the equation x = 4y + 7.
C) Solve the equation for y in terms of x.
D) Substitute y with ( f^(-1) (x) ) and express it as a function of x.

Answer 1

To find the inverse of the function f(x) = 4x + 7, rewrite it as y = 4x + 7, interchange x and y to get x = 4y + 7, solve for y to find y = (x - 7) / 4, and finally, express the inverse function as f^(-1)(x) = (x - 7) / 4.

Step-by-step explanation:

Finding the inverse of a function involves a few specific steps. Here is the process you would use to find the inverse of the linear function f(x) = 4x + 7, organized in the correct order:

1. Rewrite the equation as y = 4x + 7 (Step A).
2. Interchange x and y to form the equation x = 4y + 7 (Step B).
3. Solve the equation for y in terms of x (Step C).
4. Substitute y with ( f^(-1) (x) ) and express it as a function of x (Step D).

The detailed steps for finding the inverse function of f(x) would be as follows:

1. Let y = f(x) so we have y = 4x + 7.
2. Switch x and y to find the inverse: x = 4y + 7.
3. Solve for y: y = (x - 7) / 4.
4. Replace y with f^(-1)(x) to get f^(-1)(x) = (x - 7) / 4.