Question

f(x) = x + 2 g(x) = x - 4
(fg)(x) =
○ 2x - 2
○ x² - 8
○ x² - 2x - 8
○ x² + 2x - 8

Explanation:

Step1: Recall function multiplication

To find \((fg)(x)\), we multiply \(f(x)\) and \(g(x)\). Given \(f(x)=x + 2\) and \(g(x)=x - 4\), so \((fg)(x)=f(x)\times g(x)\).

Step2: Expand the product

Using the distributive property (FOIL method): \((x + 2)(x - 4)=x\times x+x\times(-4)+2\times x+2\times(-4)\)
Simplify each term: \(x^2-4x + 2x-8\)
Combine like terms: \(x^2-2x - 8\)

Answer:

\(x^2 - 2x - 8\) (corresponding to the option \(x^2 - 2x - 8\))