Question

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

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

(a) (f+g)(x)
(b) (f-g)(x)
(c) (fg)(x)
(d) (f/g)(x)

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 ∈ R

B. (f - g)(x) = (-4x + 1) - (3x + 1)
(f - g)(x) = (-4x - 3x) + (1 - 1)
(f - g)(x) = -7x
Domain: (-∞, ∞) x

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 ∈ R

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