1.6 Composite functions

Front

What is 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 another. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you evaluate a composite function?

Back

To evaluate a composite function (f ∘ g)(x), first evaluate g(x) and then substitute that result into f.

Front

Given f(x) = 2x^2 + 5x - 17, find f(-1).

Back

f(-1) = -20.

Front

Given f(x) = 3x + 10 and g(x) = x - 2, find f(g(5)).

Back

f(g(5)) = 19.

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 h(a) = 3 - 2a, find h(-3).

Back

h(-3) = 9.

Front

Given f(x) = 3x + 10 and g(x) = x - 2, find g(f(-10)).

Back

g(f(-10)) = None of these.

Front

If f(n) = 2n + 1 and g(n) = 3n, find f(n) + g(n).

Back

f(n) + g(n) = 5n + 1.

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

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.