Question

Use f(x) and g(x) to find a formula for each expression. Identify its domain.

Answer 1

F(x) = -4x + 1
g(x) = 3x + 1

A. (f + g)(x) = (-4x + 1) + (3x + 1)
    (f + g)(x) = (-4x + 3x) + (1 + 1)
    (f + g)(x) = x + 2
    Domain: (-∞, ∞) {x|x ∈ R}

B. (f - g)(x) = (-4x + 1) - (3x + 1)
    (f - g)(x) = (-4x - 3x) + (1 - 1)
    (f - g)(x) = -7x
    Domain: (-∞, ∞) {x|x ∈ R}

C. (f · g)(x) = (-4x + 1)(3x + 1)
    (f · g)(x) = -4x(3x + 1) + 1(3x + 1)
    (f · g)(x) = -4x(3x) - 4x(1) + 1(3x) + 1(1)
    (f · g)(x) = -12x² - 4x + 3x + 1
    (f · g)(x) = -12x² - x + 1
    Domain: (-∞, ∞) {x|x ∈ R}

D. (f ÷ g)(x) = (-4x + 1) ÷ (3x + 1)
     Domain: (-∞, ⁻¹/₃) U (⁻¹/₃, ∞) {x|x ≠ ⁻¹/₃}