Find (f g) (x) (g f) (x) and (f g) (3)

13. f(x) = 2x g(x) = x + 5

14. f(x) = 4x g(x) = x - 3

15. f(x) = 2x + 1 , g(x) = 3x - 2

16. f(x) = 5x - 3 g(x) = x ^ 2 - 3

Answer:Here's the solution for each problem, showing the steps to find (f ∘ g)(x), (g ∘ f)(x), and (f ∘ g)(3): 13. f(x) = 2x, g(x) = x + 5 - (f ∘ g)(x): This means f(g(x)). Substitute g(x) into f(x): f(g(x)) = 2(x + 5) = 2x + 10- (g ∘ f)(x): This means g(f(x)). Substitute f(x) into g(x): g(f(x)) = (2x) + 5 = 2x + 5- (f ∘ g)(3): Substitute 3 into (f ∘ g)(x): 2(3) + 10 = 16 14. f(x) = 4x, g(x) = x - 3 - (f ∘ g)(x): f(g(x)) = 4(x - 3) = 4x - 12- (g ∘ f)(x): g(f(x)) = (4x) - 3 = 4x - 3- (f ∘ g)(3): 4(3) - 12 = 0 15. f(x) = 2x + 1, g(x) = 3x - 2 - (f ∘ g)(x): f(g(x)) = 2(3x - 2) + 1 = 6x - 4 + 1 = 6x - 3- (g ∘ f)(x): g(f(x)) = 3(2x + 1) - 2 = 6x + 3 - 2 = 6x + 1- (f ∘ g)(3): 6(3) - 3 = 15 16. f(x) = 5x - 3, g(x) = x² - 3 - (f ∘ g)(x): f(g(x)) = 5(x² - 3) - 3 = 5x² - 15 - 3 = 5x² - 18- (g ∘ f)(x): g(f(x)) = (5x - 3)² - 3 = 25x² - 30x + 9 - 3 = 25x² - 30x + 6- (f ∘ g)(3): 5(3)² - 18 = 5(9) - 18 = 45 - 18 = 27

Answered by daniellejolain2930 | 2025-07-10