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# Points to Remember

Mathematics : Relation and Function: Points to Remember

Points to Remember

The Cartesian Product of A with B is defined as A × B = {(a , b) | for all a A, b B}

A relation R from A to B is always a subset of A ×B . That is R A ×B

A relation R from X to Y is a function if for every x X there exists only one y Y .

A function can be represented by

(i) an arrow diagram

(ii) a tabular form

(ii) a set of ordered pairs

(iv) a graphical form

Some types of functions

(i) One-one function

(ii) Onto function

(iii) Many-one function

(iv) Into function

Identity function f (x ) = x

Reciprocal function f (x ) = 1/x

Constant function f (x ) = c

Linear function f (x) = ax +b , a 0

Quadratic function  f (x ) = ax 2  +bx +c , a 0

Cubic function  f (x ) = ax 3  +bx 2  + cx +d , a 0

For three non-empty sets A, B and C, if f : A B and g : B C are two functions, then the composition of f and g is a function g f : A C will be defined as g o f (x ) = g( f (x )) for all x A .

If f and g are any two functions, then in general, f o g g o f

If f, g and h are any three functions, then f  o (g o h ) = ( f o g ) o h

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10th Mathematics : UNIT 1 : Relation and Function : Points to Remember | Relation and Function | Mathematics