Class 12 Relations And Functions · Short Answer2 Markstypes_of_functions
Class 12 Maths · Relations And Functions · Short Answer #170
For n∈N, f(n)=(n+1)/2 when n is odd, and n/2 when n is even. Is f:N→N bijective?
✅ Step-by-Step Solution
Final Answer: Onto but not one-one.
- For each positive integer k, the even input n=2k is in N.
- Then f(2k)=k, proving surjectivity. However f(1)=f(2)=1 with distinct inputs.
- Thus f is onto but not one-one, and is not bijective.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] For each positive integer k, the even input n=2k is in N.
- [1 mark] Then f(2k)=k, proving surjectivity. However f(1)=f(2)=1 with distinct inputs.
- [0.5 marks] Thus f is onto but not one-one, and is not bijective.
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