Facts about function composition, Algebra

We have to note a couple of things here regarding function composition. 

Primary it is NOT multiplication. Regardless of what the notation may recommend to you it is simply not multiplication.

Second, the order which we've listed the two functions are very important as more frequently than not we will get distinct answers based on the order we've listed them.

At last, function composition is actually nothing more than function evaluation. All we're actually doing is plugging the second function listed in first function listed.  In the definitions we used [  ] for the function evaluation rather than the standard (  ) to ignore confusion with too several sets of parenthesis, however the evaluation will work the similar.

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