Composite Functions

Front

What is a composite function?

Back

A composite function is a function that is formed by combining two functions, denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find f(g(x))?

Back

To find f(g(x)), substitute g(x) into the function f(x).

Front

Given f(x) = -3x + 7 and g(x) = 2x² - 8, find f(g(x)).

Back

f(g(x)) = -6x² + 31.

Front

Given f(x) = 2x and g(x) = x² + 3, find f(g(x)).

Back

f(g(x)) = 2x² + 6.

Front

What is the notation for composite functions?

Back

The notation for composite functions is f(g(x)) or (f ∘ g)(x).

Front

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

Back

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

Front

What is the output of h(a) = 3 - 2a when a = -3?

Back

h(-3) = 9.

Front

Which of the following is the same as fοg(x)?

Back

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

What is the range of a composite function?

Back

The range of a composite function is determined by the range of the outer function after applying the inner function.