Question

Which of the following expressions is the inverse of the function y = f(x) = 2x - 6?

A. x = f(y) = 2y + 6
B. x = f(y) = (y + 6)/2
C. x = f(y) = (y - 6)/2
D. x = f(y) = -2y + 6

Answer 1

To find the inverse of the function y = 2x - 6, switch x and y to get x = 2y - 6, then solve for y to get y = (x + 6) / 2, leading to the answer x = (y + 6) / 2, which is option B.

Step-by-step explanation:

The inverse of the function y = f(x) = 2x - 6 is found by solving for x in terms of y. This is done by swapping the x and y in the equation and then solving for x. So starting with the original function,

1. Swap x and y: x = 2y - 6.
2. Solve for y: y = (x + 6) / 2.

Thus, the inverse function is x = f(y) = (y + 6) / 2, which corresponds to option B.