Answer to Question #276428 in Discrete Mathematics for Ditther Gacula

Question

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.

$f\circ g=2x+1-3=2x-2$

2.

$f\circ h=x^2-5-3=x^2-8$

3.

$h\circ g=(2x+1)^2-5=4x^2+4x-4$

4.

$g\circ f=2(x-3)+1=2x-5$

5.

$g\circ h=2(x^2-5)+1=2x^2-9$