(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 = \{(1,

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

(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 $R = \{(1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7)\}$,each element of the domain $\{1, 2, 3, 4, 5, 6\}$ is associated with a unique element in the range $\{2, 3, 4, 5, 6, 7\}$.Since no two ordered pairs have the same first element,every input has exactly one output.Therefore,the relation 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:
$R = \{(1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7)\}$

A
It is a function because every element in the domain has a unique image in the codomain.
B
It is not a function because the domain elements are not distinct.
C
It is a function because the range elements are distinct.
D
It is not a function because the relation is not symmetric.

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Relations and Functions

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Defination of Function

Let $A = \{a, b, c, d\}$ and $B = \{1, 2, 3\}$. The relations $R_1, R_2, R_3, R_4$ are defined as follows:
$R_1 = \{(a, 1), (b, 2), (c, 1), (d, 2)\}$
$R_2 = \{(a, 1), (b, 1), (c, 1), (d, 1)\}$
$R_3 = \{(a, 2), (b, 3), (c, 2), (d, 2)\}$
$R_4 = \{(a, 1), (b, 2), (a, 2), (d, 3)\}$
Which of the following is true?

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Let $A = \{1, 2, 3, 4\}$,$B = \{1, 5, 9, 11, 15, 16\}$ and $f = \{(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)\}$. Is $f$ a function from $A$ to $B$? Justify your answer.

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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.

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$A$ function $f$ is defined by $f(x) = 2x - 5$. Find the values of $f(0)$,$f(7)$,and $f(-3)$.

Easy

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Let $f(x)$ be a polynomial with integer coefficients satisfying $f(1)=5$ and $f(2)=7$. The smallest possible positive value of $f(12)$ is

DifficultKVPY 2017

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Examine the following relation and state whether it is a function or not,giving reasons:$R = \{(1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7)\}$

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Let $A = \{1, 2, 3, 4\}$,$B = \{1, 5, 9, 11, 15, 16\}$ and $f = \{(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)\}$. Is $f$ a function from $A$ to $B$? Justify your answer.

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.

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Examine the following relation and state whether it is a function or not,giving reasons:
$R = \{(1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7)\}$