A function is given:

f (x) = 3x + 12

a. Determine the inverse of this function and name it g (x).

b. Use composite functions to show that these functions are inverses.

c. Evaluate f (g (-2)). Explain: What is the domain?

We are given the function to name as f (x) equal to 3x + 12 and we are asked to find the inverse of the function and name it g (x). first step is to extract x, this is equal to (y - 12) / 3 = x; then exchange the places of x and y, that is (x - 12) / 3 = y = g (x). we evaluate f (g (-2)). f (g (x)) is equal to 3 * ((x - 12) / 3) + 12 = x - 12 + 12 = x. The domain is from negative infinity to positive infinity