Composite Functions Flashcards

A way to represent functions, typically written as f(x), where f is the function and x is the input.

A function created by combining two functions, where the output of one function becomes the input of another.

Composite functions are written as (f ∘ g)(x), which means f(g(x)).

In (f ∘ g)(x), calculate g(x) first, then use the result as the input for f(x).

If f(x) = 2x + 3 and g(x) = x^2, then (f ∘ g)(x) = f(g(x)) = f(x^2) = 2(x^2) + 3.

To evaluate (f ∘ g)(x) for a specific x, first calculate g(x), then substitute the result into f(x).

The inverse of a composite function (f ∘ g)(x) is not simply the inverse of f(x) or g(x); it requires reversing the operations in the correct order.

The domain of (f ∘ g)(x) is the set of x-values for which g(x) is defined and f(g(x)) is also defined.

The range of (f ∘ g)(x) depends on the range of g(x) and how it maps through f(x).

If g(x) represents the time it takes to travel a distance and f(x) represents the cost of travel based on time, then (f ∘ g)(x) gives the cost based on distance.