a polynomial function.( Why ?) Example Define the function f : R → R by y = f ( x ) = x , x ∈ R . Complete the Table given below by using this definition. What is the domain and range of this function? Draw the graph of f .
– – – – y = f ( x ) = x Solution The completed Table is given below: – – – – y = f ( x ) = x Domain of f = { x : x ∈ R }. Range of f = { x : x ∈ R }. The graph of f is given by Fig . Fig .
MATHEMATICS Example Draw the graph of the function f : R → R defined by f ( x ) = x , x ∈ R . Solution We have f ( ) = , f ( ) = , f (– ) = – , f ( ) = , f (– ) = – , f ( ) = ; f (– ) = – , etc. Therefore, f = {( x , x ): x ∈ R }. The graph of f is given in Fig .
. Fig . (iv) Rational functions are functions of the type f x g x , where f ( x ) and g ( x ) are polynomial functions of x defined in a domain, where g ( x ) ≠ . Example Define the real valued function f : R – { } → R defined by ( ) = f x x , x ∈ R –{ }.
Complete the Table given below using this definition. What is the domain and range of this function? – – . – – .
Solution The completed Table is given by – – . – – . . .
. RELATIONS AND FUNCTIONS The domain is all real numbers