ACTIVITY 2 Let f(x) = 2x-1, g(x) = x ^ 2 - 2x + 1 Find a. (f g) (x) b. (g f) (x) c. (f f) (- 1) d. ( (g g) (2) e. (f g) (- 3)

Step-by-step explanation:Function CompositionUnderstanding the Notation * (f ∘ g)(x) means "f of g of x" or "apply g first, then apply f." * (g ∘ f)(x) means "g of f of x" or "apply f first, then apply g."Given functions: * f(x) = 2x - 1 * g(x) = x² - 2x + 1Solutions:a. (f ∘ g)(x) * We substitute g(x) into f(x): * f(g(x)) = f(x² - 2x + 1) = 2(x² - 2x + 1) - 1 * Simplifying: 2x² - 4x + 1b. (g ∘ f)(x) * We substitute f(x) into g(x): * g(f(x)) = g(2x - 1) = (2x - 1)² - 2(2x - 1) + 1 * Simplifying: 4x² - 4x + 1c. (f ∘ f)(-1) * First, find f(-1): f(-1) = 2(-1) - 1 = -3 * Then, substitute -3 into f(x): f(-3) = 2(-3) - 1 = -7 * So, (f ∘ f)(-1) = -7d. (g ∘ g)(2) * First, find g(2): g(2) = 2² - 2(2) + 1 = 1 * Then, substitute 1 into g(x): g(1) = 1² - 2(1) + 1 = 0 * So, (g ∘ g)(2) = 0e. (f ∘ g)(-3) * First, find g(-3): g(-3) = (-3)² - 2(-3) + 1 = 16 * Then, substitute 16 into f(x): f(16) = 2(16) - 1 = 31 * So, (f ∘ g)(-3) = 31

Answered by garciakyle6789 | 2024-09-08