Composition of functions

Front

What is the composition of functions?

Back

The composition of functions is a way to combine two functions, where the output of one function becomes the input of another. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

Given f(x) = x^2 + 4 and g(x) = x + 5, find f ∘ g(x).

Back

f ∘ g(x) = (g(x))^2 + 4 = (x + 5)^2 + 4 = x^2 + 10x + 29.

Front

How do you evaluate f(g(8)) if f(x) = x^2 + 4 and g(x) = x + 5?

Back

First, find g(8): g(8) = 8 + 5 = 13. Then, find f(13): f(13) = 13^2 + 4 = 169 + 4 = 173.

Front

If f(x) = 2x + 3 and g(x) = -3x - 4, find f(g(x)).

Back

f(g(x)) = f(-3x - 4) = 2(-3x - 4) + 3 = -6x - 8 + 3 = -6x - 5.

Front

Evaluate f(g(0)) if f(x) = 3x + 10 and g(x) = x - 2.

Back

g(0) = 0 - 2 = -2. Then, f(-2) = 3(-2) + 10 = -6 + 10 = 4.

Front

Given g(x) = x^2 - 2x and h(x) = x - 2, find g ∘ h(x).

Back

g(h(x)) = g(x - 2) = (x - 2)^2 - 2(x - 2) = x^2 - 4x + 4 - 2x + 4 = x^2 - 6x + 8.

Front

What is the notation for the composition of functions?

Back

The notation for the composition of functions is f ∘ g, which means 'f of g'.

Front

How do you find the composition of two functions?

Back

To find the composition of two functions f and g, substitute g(x) into f(x): (f ∘ g)(x) = f(g(x)).

Front

What is the domain of the composition of functions?

Back

The domain of the composition f ∘ g is the set of all x in the domain of g such that g(x) is in the domain of f.

Front

If f(x) = x + 1 and g(x) = 2x, what is f(g(x))?

Back

f(g(x)) = f(2x) = 2x + 1.