(A) relation $R$ from a set $A$ to a set $B$ is a function if every element of $A$ has one and only one image in $B$.In the given relation $R = \{(2,

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It is a function because each element in the domain has a unique image.

(A) relation $R$ from a set $A$ to a set $B$ is a function if every element of $A$ has one and only one image in $B$.In the given relation $R = \{(2, 1), (3, 1), (4, 2)\}$,the domain is $\{2, 3, 4\}$.For each element in the domain:- The image of $2$ is $1$.- The image of $3$ is $1$.- The image of $4$ is $2$.Since each element in the domain has a unique image in the codomain,the relation $R$ is a function.

Class 11 Mathematics Relations and Functions Defination of Function

Easy

Examine the following relation and state whether it is a function or not,giving reasons:
$R = \{(2, 1), (3, 1), (4, 2)\}$

A
It is a function because each element in the domain has a unique image.
B
It is not a function because the element $1$ is repeated in the range.
C
It is not a function because the element $2$ is repeated in the domain.
D
It is not a function because the relation is not one-to-one.

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Relations and Functions

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Defination of Function

Let $f$ be the subset of $Z \times Z$ defined by $f = \{(ab, a+b) : a, b \in Z\}$. Is $f$ a function from $Z$ to $Z$? Justify your answer.

Medium

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The function $t$ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $t(C) = \frac{9C}{5} + 32$. Find $t(-10)$.

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Statement $1$ : If $A$ and $B$ are two sets having $p$ and $q$ elements respectively,where $q > p$. Then the total number of functions from set $A$ to set $B$ is $q^p$.
Statement $2$ : The total number of selections of $p$ different objects out of $q$ objects is ${}^qC_p$.

DifficultAIEEE 2012

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If $Q$ denotes the set of all rational numbers and $f\left(\frac{p}{q}\right)=\sqrt{p^2-q^2}$ for any $\frac{p}{q} \in Q$, then observe the following statements.
$I$. $f\left(\frac{p}{q}\right)$ is real for each $\frac{p}{q} \in Q$.
$II$. $f\left(\frac{p}{q}\right)$ is a complex number for each $\frac{p}{q} \in Q$.
Which of the following is correct?

MediumTS EAMCET 2007

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Let $f: X \rightarrow Y$ be a function and $A_y = f^{-1}(\{y\})$ for $y \in Y$. Then $A_i \cap A_j = \phi$ $(i \neq j)$ for all $i, j \in Y$ and $\bigcup_{y \in Y} A_y = X$, if

EasyTS EAMCET 2019

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Examine the following relation and state whether it is a function or not,giving reasons:$R = \{(2, 1), (3, 1), (4, 2)\}$

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Let $f$ be the subset of $Z \times Z$ defined by $f = \{(ab, a+b) : a, b \in Z\}$. Is $f$ a function from $Z$ to $Z$? Justify your answer.

The function $t$ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $t(C) = \frac{9C}{5} + 32$. Find $t(-10)$.

Statement $1$ : If $A$ and $B$ are two sets having $p$ and $q$ elements respectively,where $q > p$. Then the total number of functions from set $A$ to set $B$ is $q^p$.Statement $2$ : The total number of selections of $p$ different objects out of $q$ objects is ${}^qC_p$.

Let $f: X \rightarrow Y$ be a function and $A_y = f^{-1}(\{y\})$ for $y \in Y$. Then $A_i \cap A_j = \phi$ $(i \neq j)$ for all $i, j \in Y$ and $\bigcup_{y \in Y} A_y = X$, if

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Examine the following relation and state whether it is a function or not,giving reasons:
$R = \{(2, 1), (3, 1), (4, 2)\}$

Statement $1$ : If $A$ and $B$ are two sets having $p$ and $q$ elements respectively,where $q > p$. Then the total number of functions from set $A$ to set $B$ is $q^p$.
Statement $2$ : The total number of selections of $p$ different objects out of $q$ objects is ${}^qC_p$.