Answer to Question #276430 in Discrete Mathematics for Ditther Gacula

Question

B. Exercises: Let f(x) = x – 3 , g(x) = 2x + 1 and h(x) = x2 – 5. Find the following 1. f ₒ g 2. f ₒ h 3. h ₒ g 4. g ₒ f 5. g ₒ h 

Answer 1

$1. fog=2x+1-3=2x-2\\ 2. foh=x^2-5-3=x^2-8\\ 3. hog=(2x+1)^2-5=4x^2+1+4x-5=4x^2+4x-4=4(x^2+x-1)\\ 4. gof=2(x-3)+1=2x-6+1=2x-5\\ 5. goh=2(x^2-5)+1=2x^2-10+1=2x^2-9$