Question

Given f(x) = 1/2 * x - 3, the inverse of f(x) is f^(-1)(x) = 2x + 3 where the domain is all integers x such that 4 ≤ x ≤ 7, which of the following is NOT a representation for f^(-1)(x)?

A. f^(-1)(x) = 2x + 3
B. f^(-1)(x) = 7 - 2x
C. f^(-1)(x) = (x + 3)/2
D. f^(-1)(x) = 2(x - 1) + 1

Answer 1

The inverse of the function can be found by switching the roles of x and y and solving for y. The correct representation is f^(-1)(x) = 2x + 3. Option B is not a representation for the inverse function.

Step-by-step explanation:

The inverse of the function f(x) = 1/2 * x - 3 can be found by switching the roles of x and y in the equation and solving for y. The correct representation of f^(-1)(x) is f^(-1)(x) = 2x + 3.

To find the inverse function, we start with the equation y = 1/2 * x - 3 and switch the roles of x and y to get x = 1/2 * y - 3. Then we solve for y by isolating it: x + 3 = 1/2 * y, 2(x + 3) = y, and y = 2x + 6. Finally, we replace y with f^(-1)(x) to get f^(-1)(x) = 2x + 3.

Option B, f^(-1)(x) = 7 - 2x, is not a representation for the inverse function of f(x), so the answer is B.