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 (g ∘ f)(x) = g(f(x)).

Front

How do you evaluate a composite function?

Back

To evaluate a composite function g(f(x)), first evaluate f(x) for a given x, then take that result and substitute it into g.

Front

What is the notation for composite functions?

Back

The notation for composite functions is (g ∘ f)(x), which means g(f(x)).

Front

If f(x) = 2x + 3 and g(x) = x^2, what is g(f(2))?

Back

g(f(2)) = g(2(2) + 3) = g(7) = 7^2 = 49.

Front

What is the domain of a composite function?

Back

The domain of a composite function g(f(x)) is the set of all x in the domain of f such that f(x) is in the domain of g.

Front

If f(x) = x - 1 and g(x) = 3x, find g(f(4)).

Back

g(f(4)) = g(4 - 1) = g(3) = 3(3) = 9.

Front

What is the range of a composite function?

Back

The range of a composite function g(f(x)) is the set of all possible outputs of g(f(x)) as x varies over the domain of f.

Front

If f(x) = x^2 and g(x) = x + 1, what is (g ∘ f)(2)?

Back

(g ∘ f)(2) = g(f(2)) = g(2^2) = g(4) = 4 + 1 = 5.

Front

What is the importance of composite functions in real-world applications?

Back

Composite functions are used in various fields such as physics, engineering, and economics to model complex relationships between variables.

Front

If f(x) = 3x + 1 and g(x) = x/2, find g(f(-1)).

Back

g(f(-1)) = g(3(-1) + 1) = g(-2) = -2/2 = -1.