5.6 Composition of functions

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What is a function composition?

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Function composition is the process of combining two functions, where the output of one function becomes the input of another. It is denoted as (f ∘ g)(x) = f(g(x)).

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How do you denote the composition of functions f and g?

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The composition of functions f and g is denoted as (f ∘ g)(x) or g(f(x)).

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What is the domain of a composite function?

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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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If h(x) = g(f(x)), what is the order of operations?

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In the composition h(x) = g(f(x)), you first apply f to x, and then apply g to the result of f(x).

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What is the range of a composite function?

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The range of a composite function f(g(x)) is the set of all possible outputs of f for the outputs of g.

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What is the significance of the order of functions in composition?

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The order of functions in composition matters because changing the order can lead to different results. (f ∘ g)(x) is not necessarily equal to (g ∘ f)(x).

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What is an example of a function that cannot be composed with another function?

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How do you find the inverse of a composite function?

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To find the inverse of a composite function, you can use the property (f ∘ g)^{-1} = g^{-1} ∘ f^{-1}.