Functions

Now let us talk about functions. Here we will present some fundamental facts regarding functions which will help you refresh your knowledge. We will look at several examples of functions & shall also define inverse functions. Let us begin with the definition.

Definition and Examples

Definition

If X & Y are two non-empty sets, a function f from X to Y is a rule or a correspondence which linked every member of X to a unique member of Y. We write down f: X → Y (reads it as "f is a function from X to Y" or "f is a function of X into Y"). X is known as the domain and Y is called upon the co-domain of f. We will denote by f (x) that unique element of Y, which corresponds to x ∈ X.

The below described examples will help you in understanding this definition better.

Example 1

Let f: N → R described by f (x) = - x. Is "f" a function?

Solution

"f" is a function as the rule f (x) = - x relates a unique member (- x) of R to every member x of N. Here the domain is N and the co-domain is R.

Example 2

Let f : N → Z, described by the rule

Solution

 if (x) = x . Is "f" a function?

 "f " is not a function from N to Z like odd natural numbers as 1, 3, 5 . . . from N cannot be connected with any member of Z.