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Composite Functions

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Prerequisite Material:


Composite Functions:

Definition: a function made of up of two or more other functions, where the output of one is the input to the other and so on.


If f(x)=x+2, then f(3)=3+2=5.
We could take this output and enter it into another function, say, g(x)=3x-4.
Entering the value from f(x), then g(5)=3×5-4=11 .

The same result can be found by substituting f(x) into g(x)

g(f(x)) =g(x+2) =3(x+2)-4 =3x+2

So, if x=3 then g(f(3)) =3×3+2 =11 .
That is the same as before.

An alternate way of writing g(f(x)) can be written as gf(x) .
Note: the function f is worked out before g.

In general gf(x) is not the same as fg(x).


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Further Reading:

Inverse Functions

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