A function is a rule that connects inputs and outputs. Every input has one corresponding value of an output.
f(x) means a function of x. x is the input
f(x) = x2 + 3 means a functions of x where you square x and then add 3 to it.
If you want to work out the output when the input is 3, we write it like this f(3)= 32 + 3 = 9 + 3 = 12.
Sometimes the input is an algebraic term. If this is the case, replace each letter x with the desired input.
Let's write the function written above f(x) = x2 + 3 as a function with input 4x:
f(4x) = (4x)2 + 3 = 16x2 + 3