Home
Class 12
MATHS
The function f: NvecN(N is the set of na...

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

Text Solution

Verified by Experts

(i) To test whether f is one-one (injective):
Let `x_(1), x_(2) in` domain N.
Let `f(x_(1)) = f (x_(2)) rArr 2x_(1) + 3 = 2x_(2) + 3 rArr x_(1) = x_(2)`. Hence f is injective.
(ii) To rest whether f is onto (surjective) :
Let `y in` co-domain `N rArr y` is a natural number. brgt Let `y = f(x) rArr y = 2x + 3 rArr x = (y - 3)/(2) cancelin` domain N, when y = 2.
Thus `2 in` co-domain N is not the image of any `x in` domain N and hence f is not onto (surjective).
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise Try Yourself|70 Videos

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section - A) Objective Type Questions (one option is correct)|102 Videos

  • PROBABILITY

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT SECTION-J (aakash challengers questions)|11 Videos

  • SEQUENCES AND SERIES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (SECTION - J) Aakash Challengers|11 Videos

Similar Questions

Explore conceptually related problems

f: R->R given by f(x)=x+sqrt(x^2) is (a) injective (b) surjective (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 injective but not surjective surjective but not injective bijective none of these (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.

Let A={x in R :-1lt=xlt=1}=B . Then, the mapping f: A->B given by f(x)=x|x| is (a) injective but not surjective (b) surjective but not injective (c) bijective (d) none of these

Let A={x in R :-1lt=xlt=1}=B . Then, the mapping f: A->B given by f(x)=x|x| is (a) injective but not surjective (b) surjective but not injective (c) bijective (d) none of these

A function f from the set of natural numbers to integers is defined by n when n is odd f(n) =3, when n is even Then f is (b) one-one but not onto a) neither one-one nor onto (c) onto but not one-one (d) one-one and onto both

If n is a natural number, then 9^(2n)-4^(2n) is always divisible by (a) 5 (b) 13 (c) both 5 and 13 (d) none of these

The function f: R->R , f(x)=x^2 is (a) injective but not surjective (b) surjective but not injective (c) injective as well as surjective (d) neither injective nor surjective

Classify f: R->R , defined by f(x)=3-4x as injection, surjection or bijection.

A function f from the set of natural numbers to 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 is (a) neither one-one nor onto (b) one-one but not onto (c) onto but not one-one (d) one-one and onto both