What is f(g(x))?

Answer 1

Provided that the range of g(x) is the domain of f(x) then it is the composite function, called f of g of x.

Note that f(g(x) ) is not the same as g(f(x).

For example, if f(x) = x + 2 and g(x( = 3*x for real x, then

f(g(x)) = f(3*x) = 3*x + 2

while g(f(x)) = g(x + 2) = 3*(x + 2) = 3*x + 6

Answer 2

That means that you first apply function "g", with the input "x". Then, you apply function "f", with the result of the previous operation.