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Home » Mark (√) against the correct answer in the following: Let Then, is A. one – one and into B. one – one and onto C. many – one and into D. many – one and onto
Mark (√) against the correct answer in the following: Let f: N \rightarrow N: f(x)=\left\{\begin{array}{l}\frac{1}{2}(n+1) \text {, when } n \text { is odd } \\ \frac{n}{2}, \text { when } n \text { is even. }\end{array}\right. Then, \mathrm{f} is
A. one – one and into
B. one – one and onto
C. many – one and into
D. many – one and onto
CBSE | Class 12 | Functions | Maths | RS Aggarwal
Mark (√) against the correct answer in the following: Let f: N \rightarrow N: f(x)=\left\{\begin{array}{l}\frac{1}{2}(n+1) \text {, when } n \text { is odd } \\ \frac{n}{2}, \text { when } n \text { is even. }\end{array}\right. Then, \mathrm{f} is
A. one – one and into
B. one – one and onto
C. many – one and into
D. many – one and onto

Solution:

Option(D) is correct.
f:\mathrm{N} \rightarrow \mathrm{N}: \mathrm{f}(\mathrm{x})=
f: N \rightarrow N: f(x)=\left\{\begin{array}{l}\frac{1}{2}(n+1) \text {, when } n \text { is odd } \\ \frac{n}{2}, \text { when } n \text { is even. }\end{array}\right.
One-One function

    \[\begin{tabular}{|l|l|} \hline When $\mathrm{n}$ is odd & When $\mathrm{n}$ is even \\ \hline $\mathrm{f}(1)=1$ & $\mathrm{f}(2)=1$ \\ \hline $\mathrm{f}(3)=2$ & $\mathrm{f}(4)=2$ \\ \hline \end{tabular}\]

Clearly from the above that the function is many-one.

Onto function
For any value of \mathrm{n} \in \mathrm{N}, The range of \mathrm{f}(\mathrm{x}) is a natural number.
Hence, \mathrm{f}(\mathrm{x}) is onto function.

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