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 , then .
We could take this output and enter it into another function, say, .
Entering the value from , then .
The same result can be found by substituting into
That is the same as before.
An alternate way of writing
can be written as
Note: the function is worked out before .
In general is not the same as .
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