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