Hello friends, today we will find the domain of these four functions to find the domain, we need to remember two things first, the denominator term will never be zero second, the term inside square root will always be positive so keeping these two points in mind, let’s find the domain of these four functions. the first function over here is f of x equals one by x minus 2 now we know that the denominator term will never be zero i.e x minus 2 is not equal to zero i.e x minus 2 is not equal to zero lets visualize this on number line. so here we have zero, one and two. But 2 will not be included here because on substituting two in the given function, the denominator will become zero which is undefined so, domain of this function includes all the numbers from minus infinity to plus infinity excluding 2 hence, domain is from minus infinity to 2, where 2 will not be included and hence we put open bracket on two for infinity we always put open bracket which is also known as small bracket union all the numbers from two to plus infinity within open brackets so, this is the domain for this function now for the second question we have 1 by x square minus x minus 6 again we will see that denominator should not be zero. i.e x square minus x minus 6 should not be equals to 0 hence solving for x square minus x minus 6 not equals to 0 which gives that x should not be equal to three and x should also not be equal to minus two we can see on number line -2 and 3 are the points on number line since after solving this equation we have two roots: -2 and 3 so all the numbers except these two points included in domain from -∞ to -2 and from -2 to 3 and from 3 to ∞ hence domain will be (-∞,-2) U (-2,3) U(3,∞) ∞ always comes with small bracket and here -2 & 3 are excluded from the domain so we use small bracket In third question we have to check for both the conditions because we have square root as well. In denominator, we have x square plus four which means that whatever number we substitute for x,

it will lead denominator to positive value only hence no possibility for zero in denominator. no further check required we need to check the condition in numerator if we look carefully at numerator, the term inside square root is x minus 1, so we need to ensure that this term is always greater than or equal to zero. assume same root in denominator, In that case we cant put equal to sign, it will create divide by zero problem So x is greater than or equal to 1 lets visualize this on number line. points are zero and one we can clearly see that the required domain becomes any number greater than or equal to one. so domain=[1,∞) since one is included in the domain so use [ bracket In next problem, we need to ensure that denominator is not zero and term inside square root is positive hence we calculate x square minus four is greater than zero. we can not write equal to zero since it will create divide by zero problem So factoring this term as x minus two and

x plus two greater than zero lets visualize this on number line. -2 and 2 are the two points -2 and 2 will not come under domain since expression is strictly greater than zero Now will check the sign of each interval take any value between -2 and 2 e.g x=1 by putting x=1, equation becomes negative. so sign between -2 and 2 becomes negative since this is a quadratic equation other two interval’s sign become positive we need only positive value since equation is strictly positive so domain becomes (-∞,-2)U(2,∞)

## 100 Comments

## DKdemy

In 2nd example there is a writing mistake: Domain will be (- ∞,-2) U (-2,3) U (3,∞) instead of (- ∞,-2) U (2,3) U (3,∞)

## Zeeshan Jan

order it up

## MAKE MONEY

2:25 pagal samjha he haame. Matlab kuch bhi

x-3 = not 0 but x=3 ….. But how😂😂

## Saurabh Singh

Bhai second wala galat hai

## Abduallah Mustafa

u have copy organic chemistry

## Abduallah Mustafa

where is range

## Rupam Saikiah

Thanks for this video 🙏

## Sk Suman

Apnar 2 question a domain a (-2,something)hoba

## Amir Rehman

thanks alot sir !!1 your video cleared all my concept

## Bishal Jena

Thank you sir

## Rojan Tamang

Thank you sir

## Movie masala

Sir that's translations are making difficult to see the sum which you are making on the board please remove translation or shift them down sir please

## shivam tripathi

Sir new topit start kijiye

## Umanga Nepal

in question no 2 , you have written (2,3) instead of (-2,3) !! its a nice video and thank you so much!

## The van Gaming

Sir if i guess u belongs to Bihar

Am i right but i dosn't matter ur teacher is fantastic luv u sir

## anisetti jagadeeswararao

Very nice explanation.

## Ankit Chauhan

#thanku_very_much🙂🙂

## Subhash Rock subhash

In 2nd example x is not equal to 3 and -2 but you wrote equal to……

## kunal kr sinha

Sir confusion hai ki Example 2. me -2 and +3 ke becha ka value le kar negative and positive define nahe kiye kyo ?

## Duaa Imran Sheikh

aik lafaz bhe nae samajh aya🤔🤔

## Dr.Sudershna Sharma

Sir 2nd example me (-2,3) hoga domain me

## Om Salpekar

2:59 it's a bit wrong… it (-2,3)

## Vijay Kumar

sir plz m bda confuse ho gya hun range or domain m ap en sbhi ka range bhi bta dijeye

## Anna Veronica Ortuoste

Where's the range? It's only domain

## Mr. Fron

When

X- 3 is not equal to 0

To X= 3 kaise ho gayega?

## Mushtaq Ahmad

bhot bhot shukrya Sir g ap ka,,,,,,,

## Avenger Resolution

Sir aap kahan se ho india mai ?

## Singh Avishas

2:23 wala data galat hai

## milind tiwari

Well explained.

## Sanjana Singh

Sir,really so helpful…Be making videos like this only sir,we will surely try to improve ourselves and can understand better than the classes we take…..Thank you so much sir🙏

## Comsian Vines

Thanks sir

but Sir g ap apna concept video bnaye about range of a function plz

## SBB YT

2:27

## Manjeet Sharma

sir why we use union while writing between two sets

## Rohit Pandey

Agar log function ho to….

## sadek shaikh

Mashaallah!!!!

## Bidhan Acharya

Infinity mai hamasha choto bracket kyu use karte hai

## Bidhan Acharya

Aur bhai

sin inverse x=y then x=siny how can this be prooved without example

## Bidhan Acharya

Aur bhai

sin inverse x=y then x=siny how can this be prooved without example

## Kanchan Kumari

Thanks

## Mo Izak

you don't explain minor details ,enjoying camra though

## lawaa salah

some word like kurdish words dw hhhhhhhhhh

really its usefill for me thankis teacher

## Selina Xetry

thank you💜

## akash sharma

Thanks, proved very helpful for me

## Divyanshu Gupta

Thnx sir

## vaishamvi singh

5:03 x should be greater than both -2 and 2 then it should be greater than 2 how can it take value less than -2

## Varun Vyas

Thank You!

## ASHOK YADAV

Thank you sir. U cleared all my doubts

## priya singhal

Thanku sir… Sirf aapka hi smj aaya ye topic:-):-)

## WEIRD NAMER

2:58 it think there is -2 instead of 2

## All About Drums

Thank u so much sirrr

## Advait Tonpe

thank u sir for this video

## Azhar Shah

Thanks sir I am from Pakistan and very thankful to you

## Deepika Saini

Voice clear n h sir

## Ranjit yadav

apne 2nd no question me sign gadbad kr diya

## piano tutorial

2:53 it is not correct

## Devdeep dhiman

Great

## ch. Adnan

Domain and range very difficult chapter

## Kapil Dev

Sir ek algebraic aur ek trigonometric function k difference ka domain Ya range kaise pta karenge, agar ek saath bahut saare function positive aur negative sign K saath ho to, domain aur range kaise likhe, reply soon

## Kuldeep Singhmeena

Itna Accha Nahi smjaya. Iss Acha to hamare school teacher smjha dete hai

## نجمة ةة

فتهمت حيييل 😂اوف يلگهر

## Saidul Islam

(- Infinite,-2) U ~(-2,3) U (3,infinite) hona chahiye sir

## Sahil Jha

Thanks sir

## Banty Panda

Thank you sir it is really helpful

## Devesh Tiwari

Best sir ji

## Ravi Kumar ranjan

Sir don't make mistakes

## Ashray Maheshwari

Thanks a lot sir great help from ur side

## Honey Singh

Sir mind blowing exlplanitation 👏👏👏👏👏👏👏👏

## Pranjal Srivastava

Nice explanation

## ALL ROUNDER

God bless you sir.

May god fill your life with happiness

## Rajinder Kumar

Bhai domain ka Matlab to bata pahle

## Nupur Parikh

In 2 nd example you write x+2#0 then how you get x=2 ? X=-2 is possible if x+2=0

## Mickky Man

For exactly 2:52 there is wrong…..

There should be (-2) in case of 2

## Piyush Sharma

wavy curve nahi ata kaya sir yeh kaya bata raha hoo

## Comedy4u

F(x)= square root x-1 divide by x2 – 2x …??? Kindly solve this sir…

## I am DuBeY

Where is range

## yusufansari_18z

Sir thankc for subtititles

## Indira Sachin

Range nahi hai

## Satyam Tiwary

Bhag sala tor samjhavalsamajh me naikhe aawat

## Rahuljethani Rahuljethani

Aap aache se samjao

## Amal fathima

And how to find range of these functions?

## Ajay Sharma

Maja nahi aaya sir

## technology videos with khosya akash

Ncert ta bhi bhar nikalo….Elements kraya kro

## Anirudh Gujjar

Bhadwa sala

## MR FAILURE

3:36 mey agar denominator under root of -4square hua tho denominator 0 hoga na sir aur value undefined hojayega.

## Obaidullah Baloch

Sir ap na last sawal ma jo < sign lgaya ha ya kasa use howa. Can you clear my this confusion

and also send me link about these types of videos < &

## Suraj Mehta

Sir ye lesson pura dimag se bahar ja raha ha

## fact of physics

Thanks sir

## Prabal Maurya

Plzz see at time 2:54 when this video is played there is a mistake of writing

## Holographic Bot

Are waah itni achi and deep explanation. Wow this is good .

Keep it up sir

## Raj Bhagat

2 no qustion ka range kese niklega

## Dheeraj Kumar meena

Sir sequence and series pe ek video bna do class11 for IIT-JEE ❤️❤️

## vivek yadav

Osm

## Akanksha Gupta

Greater than hi kyo huaa.. less than bhi to ho Sakta h

## zubaed alvi

I have a problem on 4:21…

## Imran Hussain

thank you so much sir

sirf ap he ki smj ay hy

## Shruti Tamang

Paila ma kina x doesnot belongs to 2 vayo🤔🤔🤔🤔

## Singh Amaninder

Which are the important questions/examples from NCERT for Mid Term and Finals?

## DIKSHA LOHE

Nice teaching thank you so much for my concept clearing.

## Jawad Ali

Thanks sir

## Rohan Nikam

Sir (-2,3) hona chahiyena