The composition of functions f(x) and g(x),  (fog)(x),  is the function  f(g(x)).


It means that the function g(x) works/(is applied) first to x and transform x into the other value g(x), 

which goes then as an argument / (as an input)  to the function f.



The product of the functions f(x) and g(x),  (f*g)(x), is simply the product of their values.



So, you should know that  (fog)(x)  and  (f*g)(x)  are TWO DIFFERENT functions.


Look attentively on their definitions and designations --- then you will be OK.

So, again, in order for to be totally clear.


When you call and write  " the composition of the function (f*g)(x) ",


     +-----------------------+
     |  YOU MAKE a MISTAKE.  |
     +-----------------------+



If it is a composition,  it should be written as  (fog)(x).


If it is a product, then it should be written as  (f*g)(x).