HW: Composite functions

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What is a composite function?

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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)).

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How do you find the domain of a function?

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The domain of a function is the set of all possible input values (x) for which the function is defined. To find the domain, identify any restrictions on x, such as division by zero or square roots of negative numbers.

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(f ° g)(x) = f(g(x)) = f(3x^2 - 1) = (3x^2 - 1) - 5 = 3x^2 - 6.

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What is the range of a function?

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The range of a function is the set of all possible output values (y) that the function can produce based on its domain.