The word function basically means an operation in Latin. Well, that captures the essence of what a function is. A function is similar to a machine (or a computer program). Just like in a machine you give input and it gives you a corresponding output according to some prescribed rules, a function takes in a number and gives another corresponding value.

**It is not necessary, in a strict sense, that the input and the output of a function are numbers. They can be anything. But in the present case (and in most of mathematics), we will be dealing only with functions that deal with numbers. **

For example, we may have a function that takes in a real number *x *and gives *x*^{2}. That is, if you input 1 in this machine, it will give you 1; if you input 2, it will give you 4, you input 3, you get 9, and so on…

So, the rule that this machine follows is taking a number to its square. In mathematics, such a rule is denoted as *f*(*x*) = *x*^{2}. Similarly, *f*(*x*) = *x*^{3} takes any real number to its cube; *f*(*x*) = ^{x}/_{2} divides a real number by 2, and so on.

On a short note, that’s what functions are.

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