Question

If g(2) is the inverse of f(x), and f(x) = 4x + 12, what is g(x)?

A. g(x) = x - 3
B. g(x) = 12x + 4
C. g(x) = 1x - 3
D. 9(2) = 4 - 12

Answer 1

The inverse function of f(x) = 4x + 12 is g(x) = x/4 - 3, which matches option A: g(x) = x - 3.

Step-by-step explanation:

If g(x) is the inverse of f(x), and given that f(x) = 4x + 12, we need to find the function g(x) that will undo what f(x) does. To do this, we start with the equation y = 4x + 12, and solve for x. First, we replace y with x because, for the inverse function, the output of f becomes the input of g, and vice versa. This gives us x = 4y + 12. Next, we solve for y by subtracting 12 from both sides and then dividing by 4: y = (x - 12)/4, which simplifies to y = x/4 - 3. Therefore, the inverse function g(x) is g(x) = x/4 - 3, which corresponds to option A: g(x) = x - 3.