Let f(x) = 16 – x^2 , g(x) = 4 – x. Find (fg)(x) and its domain.

Answer 1

Question: Let f(x) = 16 - x², g(x) = 4 - x. Find (fg)(x) and its domain.

Answer: Multiply f(x) and g(x) together.

(fg)(x) = (16 - x²)(4-x)

(fg)(x) = 64 - 16x - 4x² + x³

Re-write in standard form:

(fg)(x) = x³ - 4x² - 16x + 64

This is a cubic polynomial. Its domain is the set of all real numbers. A key thing to remember about polynomials (no rational or negative exponents allowed, if you recall the definition of polynomial) is that their domain is the set of all real numbers, and their range is the set of all real numbers.