Home
Class 12
MATHS
Let f:N->N be defined as f(n)= (n+1)/2 i...

Let `f:N->N` be defined as `f(n)= (n+1)/2` if n is odd and `f(n)=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 GUJARATI|Exercise EXERCISE 1.3|14 Videos

  • RELATIONS AND FUNCTIONS

    NCERT GUJARATI|Exercise EXERCISE 1.4|13 Videos

  • RELATIONS AND FUNCTIONS

    NCERT GUJARATI|Exercise EXERCISE 1.1|16 Videos

  • PROBABILITY

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|18 Videos

  • VECTOR ALGEBRA

    NCERT GUJARATI|Exercise Miscellaneous Exercise on chapter 10|18 Videos

Similar Questions

Explore conceptually related problems

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

f:Z rarrZ , f(n) ={{:((n+2)," if n is even"),((2n+1)," if n is odd" ):} State whether the function f is one - one and onto .

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

Give an example of a statement P(n) which is true for all n , justify your answer.

f: N rarr N , f(n) = (n+5)^(2) , n in N , then the function f is ............

If P(n) : 2n lt n! , n in N , then P(n) is true for all n gt= ………….. .

Let f : N to N : f(x) =2 x for all x in N Show that f is one -one and into.

Let f':N rarr R be a function defined as f'(x) = 4x^(2) + 12x + 15 . Show that f:N rarrS , where, S is the range of f, is invertible. Find the inverse of f.