Composite Functions Review

Front

Define a composite function.

Back

A composite function is a function that is formed by combining two functions, where the output of one function becomes the input of the other. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

What is the notation for composite functions?

Back

The notation for composite functions is (f ∘ g)(x), which means f(g(x)).

Front

If g(x) = 2x + 3, what is g(4)?

Back

g(4) = 2(4) + 3 = 8 + 3 = 11.

Front

If f(x) = x^2 and g(x) = x + 1, find (f ∘ g)(2).

Back

(f ∘ g)(2) = f(g(2)) = f(2 + 1) = f(3) = 3^2 = 9.

Front

What is the domain of a composite function?

Back

The domain of a composite function (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) = 3x, find (g ∘ f)(1).

Back

(g ∘ f)(1) = g(f(1)) = g(1 - 1) = g(0) = 3(0) = 0.

Front

What is the range of a composite function?

Back

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

Front

If h(x) = x^2 + 2 and g(x) = 3x - 1, find h(g(-3)).

Back

h(g(-3)) = h(3(-3) - 1) = h(-10) = (-10)^2 + 2 = 100 + 2 = 102.

Front

If f(t) = -t + 5 and g(t) = 3t + 3, find (f ∘ g)(t).

Back

(f ∘ g)(t) = f(g(t)) = f(3t + 3) = -(3t + 3) + 5 = -3t - 3 + 5 = -3t + 2.

Front

What is the composition of functions f(x) = x - 2 and g(x) = 2x - 4?

Back

(f ∘ g)(x) = f(g(x)) = f(2x - 4) = (2x - 4) - 2 = 2x - 6.