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6.2 Functions

Special relations : A and B are two non-empty sets. If each element of set the A is associated with exactly one element of set B, then this association is called a function from set A to set B.

Note :-

  1. Set A is the domain

  2. Set B is the co-domain

  3. All the elements of set B need not have association

  4. The element of set B which are associated is the set "range" of the function. Thus the range is a sub-set of co-domain.

    For example, { ( 2, 9 ) , ( 3, 13 ) } is a function
    { ( 2, 5 ), ( 3, 9 ) } is not a function

  5. The element y Î B such that the function say 'f ' associates to the element x Î A is denoted by f ( x ) i.e. y = f ( x ) and y is called the 'f ' image of x or value of 'f ' at x. The element x is also called pre-image of y. Every element of A has a unique image but each element of B need not have an image of an element in A. There can be more than one element of A which has the same image in B.

  6. We denote the range of f : A ® B by f (A) Thus f ( A ) = { f ( x ) | x Î A } Þ f ( A ) Î B.

  7. The domain variable is often referred as the independent variable and the range variable is referred to as the dependent variable.

Methods of representing a function

  1. An arrow diagram can be used.

    For example if f : x ® 3 x, x Î { 2, 3, 4 } then f can be shown as


6.1 Relations
6.2 Functions
6.3 Variation

Chapter 7

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