Composition of functions worksheet

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Let f(x) = 2x + 1 and g(x)  = 6x. Perform the composition of functions

1.     f ∘ g

2.     g ∘ f


Let f(x) = x2 + 1 and g(x)  = x - 1. Perform the composition of functions

3.     f ∘ g

4.     g ∘ f


Let f(x) = x2  and g(x)  = x 

5.     Show that f ∘ g / g ∘ f = 1

Let f(x) = x3  and g(x)  = x3 .Perform the composition of functions

6.     f ∘ g

7.     g ∘ f


Let f(x) = 4x - 3  and g(x)  = x2 + 4. Find each value.

8.     f ∘ g (2)

9.     g ∘ f (-1)


Let f(x) = x2 + 2  and g(x)  = 3x  - 8. Perform the composition of functions

9.     f ∘ f

10.     g ∘ g


Let f(x) = x2  and g(x)  = x  - 1. For which value of x is

11. f ∘ g ≥ g ∘ f ?

12. f ∘ g ≤ g ∘ f ?

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