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Let f : N → N be defined by State whether the fun...

Let f : N → N be defined by | Class 12 Mathematics Chapter Relations and Functions, Relations and Functions NCERT Solutions

Question:

Let f : N → N be defined by

State whether the function f is bijective. Justify your answer.

Answer:

f: N → N is defined as

It can be observed that:

∴ f is not one-one.

Consider a natural number (n) in co-domain N.

Case I: n is odd

∴n = 2r + 1 for some r ∈ N. Then, there exists 4r + 1∈N such that

Case II: n is even

∴n = 2r for some r ∈ N. Then,there exists 4r ∈N such that.

∴ f is onto.

Hence, f is not a bijective function

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Popular questions of class 12 Mathematics

Q: Given an example of a relation. Which is
(i) Symmetric but neither reflexive nor transitive.
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Reference examples and data from the chapter when answering questions about Relations and Functions.
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Welcome to the NCERT Solutions for Class 12 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 2 , Question 9: Let f : N → N be defined by State whether the function f is bijective. Justify ....

Let f : N → N be defined by | Class 12 Mathematics Chapter Relations and Functions, Relations and Functions NCERT Solutions

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