# 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) = x^{2} + 1 and g(x) = x - 1. Perform the composition of functions

**3.**
f ∘ g

**4.**
g ∘ f

Let f(x) = x^{2} and g(x) = x

**5.**
Show that f ∘ g / g ∘ f = 1

Let f(x) = x^{3} and g(x) = x^{3} .Perform the composition of functions

**6.**
f ∘ g

**7.**
g ∘ f

Let f(x) = 4x - 3 and g(x) = x^{2} + 4. Find each value.

**8.**
f ∘ g (2)

**9.**
g ∘ f (-1)

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

**9.**
f ∘ f

**10.**
g ∘ g

Let f(x) = x^{2} and g(x) = x - 1. For which value of x is

**11.** f ∘ g ≥ g ∘ f ?

**12.** f ∘ g ≤ g ∘ f ?