The function `f: NvecN(N` is the set of natural numbers) defined by `f(n)=2n+3i s` (a) surjective only (b) injective only (c) bijective (d) none of these

Let R be the set of real numbers. If f:R->R is a function defined by f(x)=x^2, then f is (a) injective but not surjective (b) surjective but not injective (c) bijective (d) non of these

Show that f: R->R defined by f(x)=(x-1)(x-2)(x-3) is surjective but not injective.

The relation R defined on the set N N of natural numbers by xRy iff 2x^(2) -3xy +y^(2) =0 is

A mappin f : N rarrN where N is the set of natural numbers is defined as f(n)=n^(2) for n odd f(n)=2n+1 for n even for n inN . Then f is

A function f from the set of natural numbers N to the set of integers Z is defined by f(n)={((n-1)/(2),"when n is odd"),(-(n)/(2),"when n is even"):} Then f(n) is -

A function f from the set of natural numbers to the set of integers defined by f(n)={(n-1)/2,\ w h e n\ n\ i s\ od d; -n/2,\ w h e n\ n\ i s\ e v e n (a) neither one-one nor onto (b) one-one but not onto (c) onto but not one-one (d) one-one and onto both

Let f: R->R and g: R->R be two given functions such that f is injective and g is surjective. Then which of the following is injective? (a) gof (b) fog (c) gog (d) none of these

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 N be the set of natural numbers. Define a real valued function f: N to n by f(x)=2x+1. Using this defination, complete the table given below,