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

Back

f(g(x)) = 2(x² + 3) = 2x² + 6.

Front

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

Back

f(g(x)) = -3(2x² - 8) + 7 = -6x² + 31.

Front

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

Back

g(f(x)) = 2(-3x + 7)² - 8 = 18x² - 84x + 90.

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) = 2x - 8 and g(x) = 4x, what is g(f(x))?

Back

g(f(x)) = 4(2x - 8) = 8x - 32.

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 f(g(x)) is the set of all possible output values of f(g(x)).

Front

How do you evaluate a composite function at a specific value?

Back

To evaluate a composite function at a specific value, first find g(a) and then substitute that result into f.