Its a little difficult to understand Composite function actually its basic concept plzz help me in understanding it plz plzz

Hello student,
Composite functions are not difficult to understand and are interesting too.
If we have two functions f(x) and g(x), then the composition of these functiosn is defined to be a function h(x) where h(x) = f(g(x)).
Thus, if f(x) = x², and g(x) = 3x-1, then h(x) = f(g(x)) = (3x-1)²
and if h(x) = g(f(x)) , then h(x) = 3(x²)-1
Please note, that the order holds great importance here, f(g(x)) ≠ g(f(x)).
In case of f(g(x)), you must note that the range of g is in the domian of f.
You can also have the composition of afunction with ittself.
It is written as (fof)(x) = f(f(x)).
This means first we apply f and then again f is applied on the result.
SO, if f(x) = 2x + 1, then (fof)(x) = f(f(x))
= f(2x+1)
= 2(2x+1) + 1
= 4x + 3.
This means, first substitute f in f(f(x)) i.e. operate from inside and and you get f(2x+1), then since f(x) is 2x+1, so nowconsider the term in bracket as x and put this term in place of x, so you get 2(2x+1) + 1.