(C) Testing for one-one: $f(1) = \frac{1+1}{2} = 1$ and $f(2) = \frac{2}{2} = 1$. Since $f(1) = f(2)$ for $1 \neq 2$, the function is not one-one (it

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(C) Testing for one-one: $f(1) = \frac{1+1}{2} = 1$ and $f(2) = \frac{2}{2} = 1$. Since $f(1) = f(2)$ for $1 \neq 2$, the function is not one-one (it is many-one).Testing for onto: For any $y \in N$, if $y$ is odd, we can have $n = 2y-1$, then $f(2y-1) = \frac{(2y-1)+1}{2} = y$. If $y$ is even, we can have $n = 2y$, then $f(2y) = \frac{2y}{2} = y$. Thus, for every element in the codomain, there is a pre-image in the domain. Therefore, the function is onto.

Class 12 Mathematics Relation and Function Type of Functions based on Mapping

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Let $f: N \rightarrow N$ be defined by $f(n) = \begin{cases} \frac{n+1}{2}; & \text{if } n \text{ is odd} \\ \frac{n}{2}; & \text{if } n \text{ is even} \end{cases}$, for all $n \in N$ then $f$ is $\dots \dots \dots$

GUJCET 2026 All GUJCET

A
One-one but not onto
B
One-one and onto
C
Many-one and onto
D
Neither one-one nor onto

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Class 12

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Relation and Function

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Type of Functions based on Mapping

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Let $A=\{1,3,7,9,11\}$ and $B=\{2,4,5,7,8,10,12\}$. Then the total number of one-one maps $f: A \rightarrow B$,such that $f(1)+f(3)=14$,is:

DifficultJEE MAIN 2024

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Let $A = \{0, 1, 2, 3, 4, 5, 6, 7\}$. Then the number of bijective functions $f: A \rightarrow A$ such that $f(1) + f(2) = 3 - f(3)$ is equal to $.....$

DifficultJEE MAIN 2021

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The function $f: (-\infty, \infty) \rightarrow (-\infty, \infty)$ defined by $f(x) = \frac{2^x - 2^{-x}}{2^x + 2^{-x}}$ is :

DifficultJEE MAIN 2025

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$f(x)=\frac{x}{e^x-1}+\frac{x}{2}+2 \cos ^3 \frac{x}{2}$ on $R-\{0\}$ is

EasyAP EAMCET 2019

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If $f(x) = (\frac{3}{5})^x + (\frac{4}{5})^x - 1$,$x \in R$,then the equation $f(x) = 0$ has

DifficultJEE MAIN 2014

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Let $f: N \rightarrow N$ be defined by $f(n) = \begin{cases} \frac{n+1}{2}; & \text{if } n \text{ is odd} \\ \frac{n}{2}; & \text{if } n \text{ is even} \end{cases}$, for all $n \in N$ then $f$ is $\dots \dots \dots$

Similar Questions

Let $A=\{1,3,7,9,11\}$ and $B=\{2,4,5,7,8,10,12\}$. Then the total number of one-one maps $f: A \rightarrow B$,such that $f(1)+f(3)=14$,is:

Let $A = \{0, 1, 2, 3, 4, 5, 6, 7\}$. Then the number of bijective functions $f: A \rightarrow A$ such that $f(1) + f(2) = 3 - f(3)$ is equal to $.....$

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