JEE Mains · Maths · STD 12 - 1. relation and function
Let \(\mathrm{g}: \mathrm{N} \rightarrow \mathrm{N}\) be defined as \(g(3 n+1)=3 n+2\) \(g(3 n+2)=3 n+3\) \(g(3 n+3)=3 n+1, \text { for all } n \geq 0\) Then which of the following statements is true?
- A \(\operatorname{gog} \mathrm{og}=\mathrm{g}\)
- B There exists an onto function f: \(N \rightarrow N\) such that \(fog =f\)
- C There exists a one- one function \(f: N \rightarrow N\) such that \(f o g=f\)
- D There exists an function \(f: N \rightarrow N\) such that \(gof =f\)
Answer & Solution
Correct Answer
(B) There exists an onto function f: \(N \rightarrow N\) such that \(fog =f\)
Step-by-step Solution
Detailed explanation
\(g(3 n+1)=3 n+2\) \(g(3 n+2)=3 n+3\) \(g(3 n+3)=3 n+1, n \geq 0\) For \(x=3 n+1\) \((1)\) \(\operatorname{gogog}(3 n+1)=\operatorname{gog}(3 n+2)=g(3 n+3)=3 n+1\) Similarly \(\operatorname{gogog}(3 n+2)=3 n+2\) \(\operatorname{gogog}(3 n+3)=3 n+3\) So gogog…
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