JEE Mains · Maths · STD 12 - 1. relation and function
The function \(\mathrm{f}: \mathrm{N}-\{1\} \rightarrow \mathrm{N}\); defined by \(\mathrm{f}(\mathrm{n})=\) the highest prime factor of \(n\), is :
- A both one - one onto
- B one - one only
- C onto only
- D neiter one- one nor onto
Answer & Solution
Correct Answer
(D) neiter one- one nor onto
Step-by-step Solution
Detailed explanation
\(\mathrm{f}: \mathrm{N}-\{1\} \rightarrow \mathrm{N}\) \(f(n)=\) The highest prime factor of \(n\). \(f(2)=2\) \(f(4)=2\) \(\Rightarrow\) many one \(4\) is not image of any element \(\Rightarrow\) into Hence many one and into Neither one-one nor onto.
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