Question

What is the inverse function of f(x) = -2x - 6?

a. f^-1(x) = 2x + 6
b. f^-1(x) = -2x - 3
c. f^-1(x) = 1/2x + 6
d. f^-1(x) = -1/2x - 3

Answer 1

The inverse function of f(x) = -2x - 6 is f^(-1)(x) = (x + 6) / -2.

Step-by-step explanation:

The inverse function of f(x) = -2x - 6 can be found by swapping the variables x and y and solving for y. Let's call the inverse function f^(-1)(x). So, we have: x = -2y - 6. Now, let's solve for y.

Step 1: Add 6 to both sides of the equation. x + 6 = -2y

Step 2: Divide both sides of the equation by -2. (x + 6) / -2 = y

Simplifying the equation, we get: f^(-1)(x) = (x + 6) / -2. Therefore, the correct option is c. f^(-1)(x) = 1/2x + 6.