Solution:
Option(D) is correct.
One-One function
![\[\begin{tabular}{|l|l|} \hline When $\mathrm{n}$ is odd & When $\mathrm{n}$ is even \\ \hline $\mathrm{f}(1)=1$ & $\mathrm{f}(2)=1$ \\ \hline $\mathrm{f}(3)=2$ & $\mathrm{f}(4)=2$ \\ \hline \end{tabular}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-93cfb657156d4c38aa1539b35c12bca5_l3.png "Rendered by QuickLaTeX.com")
Clearly from the above that the function is many-one.
Onto function
For any value of 
Hence,
Mark (√) against the correct answer in the following: Let 
A. one – one and into
B. one – one and onto
C. many – one and into
D. many – one and onto
