Front

Define 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 the other. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

What is the notation for composite functions?

Back

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

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Back

(f ∘ g)(x) = f(g(x)) = f(x^2) = 2(x^2) + 1 = 2x^2 + 1.

Front

Back

(g ∘ f)(x) = g(f(x)) = g(3x - 4) = (3x - 4) + 5 = 3x + 1.

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.

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Back

g(f(3)) = g(3 - 1) = g(2) = 2(2) = 4.

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Back

(f ∘ g)(-1) = f(g(-1)) = f(-1 + 3) = f(2) = 2^2 = 4.

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Back

g(f(x)) = g(x + 2) = 5(x + 2) = 5x + 10.

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Back

(f ∘ g)(2) = f(g(2)) = f(3(2) - 1) = f(5) = -5 + 4 = -1.

Front

What is the composition of functions?

Back

The composition of functions is the process of applying one function to the results of another function.