Home
Class 12
MATHS
Let f: N to N be defined by f (n) = {{:(...

Let `f: N to N` be defined by `f (n) = {{:((n +1)/( 2 ), if n " is odd" ), ( (n)/(2), "if n is even "):}`for all `n in N.`
State whether the function f is bijective. Justify your answer.

Text Solution

Verified by Experts

The correct Answer is:
NO
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT BANGLISH|Exercise EXERCISE 1.3|14 Videos
  • RELATIONS AND FUNCTIONS

    NCERT BANGLISH|Exercise EXERCISE 1.4|13 Videos
  • RELATIONS AND FUNCTIONS

    NCERT BANGLISH|Exercise EXERCISE 1.1|16 Videos
  • PROBABILITY

    NCERT BANGLISH|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|19 Videos
  • VECTOR ALGEBRA

    NCERT BANGLISH|Exercise Miscellaneous Exercise on chapter 10|19 Videos

Similar Questions

Explore conceptually related problems

Let f:N->N be defined by f(x)=x^2+x+1,x in N . Then f(x) is

Let f:Wto W be defined as f (n)=n -1, if n is odd and f (n) =n +1, if n is even. Show that f is invertible. Find the inverse of f. Here, W is the set of all whole numbers.

Find the sequence of the numbers defined by a_n={1/n , when n is odd -1/n , when n is even

Let N be the set of natural numbers and two functions f and g be defined as f, g : N to N such that : f(n)={((n+1)/(2),"if n is odd"),((n)/(2),"if n is even"):}and g(n)=n-(-1)^(n) . The fog 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 -

Find the 5th and 10th terms of the sequence [u_(n)] defined by, u_(n) = {(2n+7 "when n is odd"),(n^(2) + 1 "when n is even"):}

If f:NrarrN f(n)={(n+1)/2; when n is odd =n/2; when n is even Identify the type of function

A relation R is defined from N to N as R ={(ab,a+b): a,b in N} . Is R a function from N to N ? Justify your answer.

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

If f:{1,2,3....}->{0,+-1,+-2...} is defined by f(n)={n/2, if n is even , -((n-1)/2) if n is odd } then f^(-1)(-100) is