Class 11 Mathematics Relations and Functions Defination of Function

Medium

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.

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Vedclass pdf generator app on play store

Solution

(B) relation $f$ from a set $A$ to a set $B$ is a function if every element of $A$ has one and only one image in $B$.
Given $f = \{(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)\}$.
Here,the element $2 \in A$ is associated with two different images in $B$,which are $9$ and $11$ (i.e.,$f(2) = 9$ and $f(2) = 11$).
Since an element of the domain cannot have more than one image in the codomain,$f$ is not a function.

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Relations and Functions

Subtopic

Defination of Function

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

View Solution

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

View Solution

Let $N$ be the set of natural numbers. Define a function $f: N \rightarrow N$ by $f(x) = 2x + 1$. Using this definition,complete the table given below.

$x$ $1$ $2$ $3$ $4$ $5$ $6$ $7$

$y$ $f(1) = \dots$ $f(2) = \dots$ $f(3) = \dots$ $f(4) = \dots$ $f(5) = \dots$ $f(6) = \dots$ $f(7) = \dots$

Easy

View Solution

Which of the following represents a function?

View Solution

If $f$ is a relation from the set of positive real numbers $R_{+}$ to the set of positive real numbers $R_{+}$ defined by $f(x) = 3x^2 - 2$, then $f$ is

MediumAP EAMCET 2022

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$x$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$y$	$f(1) = \dots$	$f(2) = \dots$	$f(3) = \dots$	$f(4) = \dots$	$f(5) = \dots$	$f(6) = \dots$	$f(7) = \dots$

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.

Similar Questions

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

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.

Let $N$ be the set of natural numbers. Define a function $f: N \rightarrow N$ by $f(x) = 2x + 1$. Using this definition,complete the table given below. $x$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $y$ $f(1) = \dots$ $f(2) = \dots$ $f(3) = \dots$ $f(4) = \dots$ $f(5) = \dots$ $f(6) = \dots$ $f(7) = \dots$

Which of the following represents a function?

If $f$ is a relation from the set of positive real numbers $R_{+}$ to the set of positive real numbers $R_{+}$ defined by $f(x) = 3x^2 - 2$, then $f$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Let $N$ be the set of natural numbers. Define a function $f: N \rightarrow N$ by $f(x) = 2x + 1$. Using this definition,complete the table given below.

$x$ $1$ $2$ $3$ $4$ $5$ $6$ $7$

$y$ $f(1) = \dots$ $f(2) = \dots$ $f(3) = \dots$ $f(4) = \dots$ $f(5) = \dots$ $f(6) = \dots$ $f(7) = \dots$