Combining Functions: Products and Quotients of Functions

The functions must ____________ the same ____________ in order to multiply or divide the functions.

• functions must have the same domain

• functions must have the same range

• functions must have the same codomain

• functions must have the same derivative

Determine (f × g)(x) given the discrete functions below: f(x) = {(0, 3), (1, 6), (2, 10), (3, -5)} and g(x) = {(0, 4), (2, -2), (4, 1), (6, 3)}. (f × g)(x) = ?

• {(0, 12), (2, -20)}

• {(0, 7), (2, 8)}

• {(0, 12), (2, 20)}

• {(0, 12), (2, -20), (3, 15)}

Determine the domain and end behaviour of (f × g)(x) given f(x) = x^3 + 2x^2 + x - 1, and g(x) = -2x^3 - 4x^2 + 2.

• Domain: All real numbers; End behaviour: As x → ±∞, (f × g)(x) → ±∞

• Domain: All real numbers except x = 0; End behaviour: As x → ±∞, (f × g)(x) → ±∞

• Domain: All real numbers; End behaviour: As x → ±∞, (f × g)(x) → ∓∞

• Domain: All real numbers except x = 0; End behaviour: As x → ±∞, (f × g)(x) → ∓∞

Given f(x) = 1/x and g(x) = sqrt(x + 5): a) Determine the domain for both f(x) and g(x).

• a) Domain of f(x) is x ≠ 0; Domain of g(x) is x ≥ -5

• b) Domain of f(x) is x > 0; Domain of g(x) is x > -5

• c) Domain of f(x) is x < 0; Domain of g(x) is x ≤ -5

• d) Domain of f(x) is x = 0; Domain of g(x) is x < -5

Given f(x) = 1/x and g(x) = sqrt(x + 5), what is the equation of (f × g)(x) and its domain?

• (f × g)(x) = sqrt(x + 5)/x; Domain: x > -5, x ≠ 0

• (f × g)(x) = 1/(x * sqrt(x + 5)); Domain: x > -5

• (f × g)(x) = sqrt(x + 5)/x; Domain: x ≥ -5

• (f × g)(x) = 1/(x * sqrt(x + 5)); Domain: x > -5, x ≠ 0

Find the equation of (f + g)(x) and identify the domain.

• (f + g)(x) = f(x) + g(x), domain: all real numbers

• (f + g)(x) = f(x) - g(x), domain: all real numbers

• (f + g)(x) = f(x) * g(x), domain: all real numbers

• (f + g)(x) = f(x) / g(x), domain: all real numbers