JEE MAIN - Mathematics (2024 - 27th January Morning Shift - No. 20)
The function $f: \mathbf{N}-\{1\} \rightarrow \mathbf{N}$; defined by $f(\mathrm{n})=$ the highest prime factor of $\mathrm{n}$, is :
one-one only
neither one-one nor onto
onto only
both one-one and onto
Explanation
$$\begin{aligned} & \mathrm{f}: \mathrm{N}-\{1\} \rightarrow \mathrm{N} \\ & \mathrm{f}(\mathrm{n})=\text { The highest prime factor of } \mathrm{n} . \\ & \mathrm{f}(2)=2 \\ & \mathrm{f}(4)=2 \\ & \Rightarrow \text { many one } \\ & 4 \text { is not image of any element } \\ & \Rightarrow \text { into } \end{aligned}$$
Hence many one and into
Neither one-one nor onto.
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