How do we perform compositions of functions?

Compositions of Functions:
     Example: If f(x) = x^2 and g(x) = x+6
Find f(g(4)).
   g(4) = 4+6 = 10
f(10) = 10^2 = 100 .

Compositions with Variables:
   Example: If f(x) = x^2 and g(x) = x+4
Find f(x+4)
    f(x+4) = (x+4)^2
(x+4)(x+4)            (Distribute)
      x^2 + 4x + 4x + 16
x^2 + 8x + 16 .

The term "composition of functions" (or "composite function") refers
to the combining of functions in a manner where the output from one function
becomes the input for the next function.

In math terms, the range (the y-value answers) of one function becomes
the domain (the x-values) of the next function.

The notation used for composition is: and is read "f composed with g of x" or "f of g of x".

(Regentsprep.org)