Function can be easily defined with the help of the concept of mapping. Let *X *and Y be any two non-empty sets. “A function from X to Y is a rule or correspondence that assigns to each element of set *X, *one and only one element of set Y”. Let the correspondence be ‘f’ then mathematically we write *f:* X→Y where y = *f**(x)*, x ∈ *X *and y ∈ Y. We say that ‘y’ is the image of ‘x’ under ‘*f ‘* (or x is the pre image of y).

A mapping *f:* X→Y is said to be a function if each element in the set X has it’s image in set Y. It is possible that a few elements in the set Y are present which are not the images of any element in set X.

Every element in set X should have one and only one image. That means it is impossible to have more than one image for a specific element in set X. Functions can’t be multi-valued (A mapping that is multi-valued is called a relation from X to Y)

Click Here for Next Topic » |

Click Here for Class XII Classes Maths All Topics Notes