If `NN` be the set natural numbers, then prove that, the mapping `f: NN rarr NN` defined by ,`f(n) =n-(-1)^(n)` is a bijection.

Let NN be the set of natural numbers and D be the set of odd natural numbers. Then show that the mapping f:NN rarr D , defined by f(x)=2x-1, for all x in NN is a surjection.

Let D be the set of odd natural numbers . Then show that the mapping f:NN rarrD , defined by, f(x)=2x-3 is onto but the mapping g:ZZ rarrZZ defined by , g(x)=2x-3 is not onto.

Show that, the mapping f:NN rarr NN defined by f(x)=3x is one-one but not onto

Prove that, the function f: RR rarr RR defined by f(x)=x^(3)+3x is bijective .

Let NN be the set of natural numbers: show that the mapping f NN rarr NN given by, f(x)={(((x)+1)/(2) "when x is odd" ),((x)/(2)" when x is even"):} is many -one onto.

If R denotes the set of all real numbers then the mapping f:R to R defined by f(x)=|x| is -

Let RR be the set of real numbers and the mapping f: RR rarr RR be defined by f(x)=2x^(2) , then f^(-1) (32)=

Prove that the mapping f: RR rarr RR defined by , f(x)=x^(2)+1 for all x in RR is neither one-one nor onto.

Let NN be the set of natural number and f: NN -{1} rarr NN be defined by: f(n) = the highest prime factror of n . Show that f is a many -one into mapping