Q. 94.0( 43 Votes )

# Let f : N →

Answer :

It is given that

f : N N be defined by We can observed that: (by using the definition of f)

Thus, f(1) = f(2), where 1 ≠ 2.

Therefore, f is not one-one.

Now, let us consider a natural number (n) in co domain N.

Case I: When n is odd.

Then, n = 2r +1 for some r ϵ N.

there exist 4r + 1 ϵ N such that f(4r+1) = Case II: When n is even.

Then, n = 2r for some r ϵ N.

there exist 4r ϵ N such that f(4r) = Therefore, f is onto.

Function f is not one-one but it is onto.

Thus, Function f is not bijective function.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

Fill in theMathematics - Exemplar

State True Mathematics - Exemplar

State True Mathematics - Exemplar

State True Mathematics - Exemplar

Let A = {1, 2, 3}Mathematics - Exemplar

Show that the relMathematics - Board Papers

Let N denote the Mathematics - Board Papers