Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions is a process where one function is applied to the result of another function, denoted as (f∘g)(x) = f(g(x)).

Front

If g(x) = 3x + 4 and h(x) = 3x - 1, what is (g∘h)(x)?

Back

(g∘h)(x) = 9x + 1.

Front

What does p(q(x)) mean if p(x) = 3x + 4 and q(x) = 2x²?

Back

p(q(x)) means to substitute q(x) into p(x), resulting in p(q(x)) = 6x² + 4.

Front

How do you find g(-2) if g(x) = 3x + 4?

Back

Substitute -2 into g: g(-2) = 3(-2) + 4 = -6 + 4 = -2.

Front

What is the result of f(g(5)) if f(x) = 3x + 10 and g(x) = x - 2?

Back

f(g(5)) = f(3) = 3(3) + 10 = 19.

Front

What is (f ° f)(-2) if f(x) = 2x² - 1?

Back

(f ° f)(-2) = f(f(-2)) = f(7) = 97.

Front

What is the notation for the composition of functions?

Back

The notation for the composition of functions is (f∘g)(x).

Front

What is the domain of a composite function?

Back

The domain of a composite function (f∘g)(x) 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) = x² and g(x) = x + 1, what is (f∘g)(x)?

Back

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

Front

What is the range of a composite function?

Back

The range of a composite function (f∘g)(x) is the set of all possible outputs of f(g(x)).