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) = x^{2} + 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)= 3^{2} + 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) = x^{2} + 3 as a function with input 4x:

f(4x) = (4x)^{2} + 3 = 16x^{2} + 3