Question

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

(g(x) = 12x + 4)
(g(x) = \frac{1}{4}x - 12)
(g(x) = x - 3)
(g(x) = \frac{1}{4}x - 3)

Explanation:

Set up the inverse equation

Using the Inverse Functions knowledge point

$$
LATEXBLOCK0
$$

Solve for the inverse function

Using the Linear Inverses knowledge point

$$
LATEXBLOCK1
$$

Answer:

• (A) \(g(x) = 12x + 4\)
• (B) \(g(x) = \frac{1}{4}x - 12\)
• (C) \(g(x) = x - 3\)
• (D) \(g(x) = \frac{1}{4}x - 3\) (Correct answer)