Pre-Cal Flashcard Composite Functions

Front

Define composite functions.

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

What is the formula for finding g(f(x))?

Back

To find g(f(x)), substitute f(x) into g(x). This means you take the output of f(x) and use it as the input for g.

Front

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

Back

g(f(x)) = 18x^2 - 84x + 90.

Front

What does f - g represent in function notation?

Back

f - g represents the difference between two functions, defined as (f - g)(x) = f(x) - g(x).

Front

Given f(x) = x + 2 and g(x) = x^2 - 4, find f - g.

Back

f - g = -x^2 + x + 6.

Front

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

Back

To find f(g(x)), substitute g(x) into f(x). This means you take the output of g(x) and use it as the input for f.

Front

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

Back

f(g(x)) = -6x^2 + 31.

Front

What is the significance of the order in composite functions?

Back

The order matters because (f ∘ g)(x) is not necessarily equal to (g ∘ f)(x). The output depends on which function is applied first.

Front

Given f(x) = 3x - 6 and g(x) = x^2 + 4, find (g ∘ f)(-1).

Back

(g ∘ f)(-1) = 85.

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.