composite functions
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A function takes an input and gives you a consistent output.
Example:
*f*(x) = x^2
*f*(3) = (3)^2 = 9
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A composite function can be thought of as chained functions. You give it an input and the first function gives you an output, that output is then used as the input for the second function.
Example:
*f*(x) = x^2 , *g*(x) = 4x
*g*(*f*(x)) or (g∘f)(x) means to do *f*(x) first then *g*(x)
*g*(*f*(3)) = *g*(3^2 ) = *g*(9) = 4•9 = 36
You can swap the order too:
*f*(*g*(x)) or (f∘g)(x) means to do *g*(x) first then *f*(x)
*f*(*g*(3)) = *f*(4•3) = *f*(12) = 12^2 = 144
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You can also just combine them into a new singular function:
*g*(*f*(x)) = *g*(x^2 ) = 4•x^2
*f*(*g*(x)) = *f*(4x) = (4x)^2
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