Discrete Mathematics Lecture 8 | Domain & Range Of Function | One-One and Onto Function By GP Sir

[@abhiyadav7043]

Backbenchers k masiha ho aap.. Boht ashirwad milega apko exam k ek din pehle padhne walo se..

[@7paradoxgamer]

At 20:07 I think answer is correct because hame underroot se kabhi bhi negative value nahi milegi aur y kabhi negative nahi hoga so answer is [0,3]

[@sakshigupta8324]

Kyu for x=0 you will get +-3 na ! Then ??

[@7paradoxgamer]

​@@sakshigupta8324 chatgpt reply -The function you provided is a semicircle equation centered at the origin with a radius of 3. The range of this function represents the set of all possible y-values it can take. To determine the range, we need to find the minimum and maximum values of y for the given function. Since the function represents a semicircle, the y-values will range from the lowest point on the semicircle to the highest point. The lowest point occurs at the bottom of the semicircle, where x = 0. Plugging x = 0 into the equation, we get: y = √(9 - 0^2) = √9 = 3. So, the lowest y-value is 3. The highest point on the semicircle occurs at the top, where the x-coordinate is either 3 or -3. Plugging these values into the equation, we get: For x = 3: y = √(9 - 3^2) = √(9 - 9) = √0 = 0. For x = -3: y = √(9 - (-3)^2) = √(9 - 9) = √0 = 0. Therefore, the highest y-value is 0. Hence, the range of the function y = √(9 - x^2) is [0, 3]. aur waise bhi y=+√9-x2 hai toh y ki negative value consider nahi karenge

[@sakshigupta8324]

@@7paradoxgamer okok now clearr ! Thanks 😉👍

[@garvaggarwal6979]

answer will be (B) {R}/5

[@KanhaiyaKumar-xy5qk]

correct ans of last ques is option (b) i.e, domain = R/{5} and range is equal to R/{0}

[@Payal_Ojha]

Ye options me divide sign kyu lgaya hai.. sir ne to esa kuchh nhi btaya

[@creativebanda33]

iska mtlbr ( R -5) hota hai @@Payal_Ojha

[@shashikantmishra4130]

none of these , please check Y should be

[@user-yd3ht2fx1r]

No bro domain is = R - {5}

[@Jadupadu69]

@@Payal_Ojha real no. Maise 5 ke alawa uska meaning hai

[@gautambhartiya1722]

Sir Q.3 mein y ki range [0,3] hi hogi..cause question mein given hai Y=√(9-x²) ....iska matlab y is equal to some positive quantity matlab y greater than 0

[@RaghavAnand-ik8qe]

X=-3 rakhne par bhi y non negative hi hoga

[@anubhavpratap5639]

@@RaghavAnand-ik8qe bhai wo domain nhi range k bare me bol rhe h

[@Anujmuzix]

[-3,3] hoga

[@divergentthinker143]

​@@Anujmuzixyes❤❤

[@AnandMFCGR]

college me 1 lakh fees dene ke bad bhi aisa content nahi milta

[@Pitbulldangerous]

Bhai barbaad ho gya hai paisa to college mai bher ker

[@darshparmar5485]

Sahi kaha

[@sandippal8908]

Yes 😢😢

[@OmPrakashMaharana326]

BSC mein 1 lakh how?

[@dasharathimeher1786]

@@OmPrakashMaharana326 hlo bhai aap kaha se padhte ho

[@yogesh7947]

in Q no.2 based ondomain and range there is a error in the solution for finding range, when you were applying quadratic formula , instead of 2 we have to write 2y in the denominater and the final answer of range is [ -1/2 to 1/2] -{0}.

[@animehunter2623]

Thankyou brother

[@ayushkumarsingh2537]

​@@animehunter2623Yes, I also noticed it.

[@khushmanglani7127]

Domain = R/{5} (B) option And Range = R/{0} It takes 2 seconds to solve this question thank you so much sir for providing top notch content in free of cost 🙏🏻🙏🏻

[@ayushsinghal3195]

buddi bohot tez h tumhari

[@khushmanglani7127]

@@ayushsinghal3195I solve the question orally 😂😂

[@swatinema6342]

Range kese nikalenge...??

[@amratanshmourya130]

@@swatinema6342 its very easy find the value of x in equation and then check for real number

[@krishnajain5729]

sir b hI

[@AbidKhan-jp3eb]

Domain = R/{5} Time taken 50s

[@StudyPB2k24]

noob

[@dineshchoudharyjaat1422]

Domain = R/{5} (B) option And Range = R/{0} Thank you sir....................

[@instabecreative0507]

Ques.2 In f(x) = x/ x²+1 , range of the function will be [-½,½] - {0} Sir, please ensure that this is correct. 18:21

[@Growwithtahira]

Sir you teach very well but your old video are very helpful for me ❤

[@sandippal8908]

Sir your vibes , your excitement during solving problems give me interest to do Math❤

[@yashsarin9582]

Answer of last question should be option b as all real numbers can be placed except 5 because at 5 whole expression will tend to infinity as denominator would turn 0 but any other real value except 5 wouldn't do so Hence option b

[@shalineedhuri1309]

Critical clear ho gya sir from.this video

[@arslanrafique-jz3gl]

Sir g very good yar bhut samag ati ha ap ki

[@deepanshibansal5495]

SIR 2 waale ques. mein part a ki range [-1/2,1/2]-{0} hogi

[@arun-uw6rl]

Thankuuu so much sir 💐💐

[@AyushGola-k5n]

nice way of teaching sir. apka tarika and attitude acha lga sir.

[@aniketsatpathy1532]

B Sir, there is a slight correction in the last question the range of the function sqrt(9-x^2) would be [0,3] since the domain is [-3,3] therefore, on putting the extreme values the results is zero and on the minimal value that is 0 in domain the range will have the maximum value as 3

[@instabecreative0507]

Yes the range will be [0,3] because of the square root function @aniketsatpathy1532 Sir must have changed this by mistake.

[@ITSahilAkhade]

Sir answer is (b) Sirf 1 second me answer aagaya Amazing teaching sir ty sir

[@tariqueali3879]

Bhai explain kr skte ho kya bhai

[@prernabedla1313]

thank you so much sir ji aapki video bhut helpfull h 💯💯💯 thank you so much sir ji 💯💯💯💯

[@chhandaduttadutta827]

You are really a great teacher❤ of Mathematics

[@bbgaming7944]

domain should be [negative infinity to 4 and 6 to positive infinity] because except 5 all values satisfy the equation for a real number

[@biographytecz2274]

I think u deserve more subscriber ❤❤

[@career-for-student-life]

(C)R/{-5} is the right answer ❤

[@ultralegend686]

This is wrong right answer is R/{5}

[@BusinessAnalyticsTV]

💕You are very sincere KZbinr. Thank you for sharing information 🙂ℹ️

[@royaltytrader7628]

What will be the use of this logical maths in real life,?

[@idealgaming4034]

Thank you for your time

[@Itz_me_glory03]

Thank you sir 🙏

[@KhushbooPaswan-yo1ti]

Sir AAP itna achha kaise padhate hai ❤❤

[@nishantmishra3545]

Last din padhke pass krwa diya sir

[@DHEERAJKUMAR-ur8yw]

Sir Aap class good padate hai

[@DHEERAJKUMAR-ur8yw]

Thank you🙏🙏🙏🙏🙏

[@The_Desi_Culture]

thanku sir for sharing your lot of knowledge

[@avd_tEch]

One to one function is also called injective function

[@yashrajsinghchauhan6174]

Proposnal and predicate logic and trees graphs and combination bhi sir jaldi se cover kar di jiye uske bhi video share kariye sir external exam hai 26 ko 🙏

[@GameSynergy]

SIR 10:10 Me apne joh range likhi h voh domain honi chahiye thi set ki. Pls check it sir.🙏

[@srijansarvshresth5887]

nahin bro . Domain toh set A ko kahenge = {1,2,3,4} , but range un sabhi domain ke images ko range kehte hain jo {x,y,p} hai.

[@ravirajput7354]

Happy Teachers Day Sir

[@sahilkoirala8623]

sir an you please make some more video related to Nepal's University related topic...as I can understand the topic more by watching your video......rather than in college

[@deepanshibansal5495]

aur sir ques 3 mein part b ki range [0,3] hi hogi

[@abhirupbasu9298]

Ans . B) R/{5}

[@avdeshsingh001]

THANKYOU SIR

[@AhtishamAsif-p7k]

agr yha pr hum z+ and z- rkhay to kya eik element positive number ka aur dusra element negative number ka le gay ye explain kijye

[@arohisingh8914]

Answer-R/{5} 20 sec.

[@shivangisingh1608]

Homework ans will be B) R/{5}

[@bikashsharma2702]

Sir , pls make a video on metric space i.e. connected metric space , continuity in metric space and compact metric space. I'm not understanding the topics of metric space .kindly make a video on above topic . Pls sir 🙏

[@khushijain9785]

Option(B ) R {5} is correct answer

[@desiremovies5666]

Excellent sir

[@prathamsharma4802]

In the second last question range can't be [-3,3] because according to question y will always be positive.

[@pixie_dust2089]

no it would be -3 to 3 because y value can be -3 also and we get do not get the value less than zero

[@zaid6527]

@@pixie_dust2089 it is given that y = root(9-x^2), and we know that a real number under root can never be negative so we get from here that y>=0. and hence discard -ve values

[@sambhavjain3146]

The answer is option (b) and time taken to solve this question is 4-5 Seconds

[@ayeshakhanayeshakhan1563]

Well explained sir

[@suryashekharkumar816]

Very nice sir , please Sir all lectures upload discrite mathematics

[@abhinandanjain2399]

Thank you so much sir you are amazing shaandaar teacher.

[@sasmitasamal7539]

Thank you sir 😄😄

[@ravindermehla-Cr7]

Nice respect u sir 💕

[@LOKESHYADAV-fe2kf]

R-{5} ans b solving time 15 sec

[@Cosmickid07]

R-5 =Domain Time taken = 4sec

[@SkyV77]

R-5 would be all real number-5 including 5 itself , so 5-5=0 and that’s wrong

[@akshaypratapsingh5897]

​@@SkyV77he is saying the domain is any real number but not 5

[@yuvansh6565]

hecker hai bhai hecker

[@satyendrashukla4157]

Love so much Sir

[@KeshavKumar79589]

Sir bsc वालो की किसी दिन online class लो।।आपसे कुछ बाते करनी है ।।sir please

[@lailafroz4392]

Sir... I am very impressed with you. And clear my concepts deeply... I Wana join your online session for prepration of higher competitive exams.. please sir 🙏 guide me how I join you.

[@rafi_xoss]

last one.. range is [0,3] as y can't be negative. watch root over.

[@shalineedhuri1309]

Good evening sir

[@DHEERAJKUMAR-ur8yw]

Funtion samajh Aa gya

[@bhuppidhamii]

best explainationsir

[@cricketworld4849]

Helpful!

[@masumasultana1177]

Sir we need video on Bsc 4th semester under guwahati university...plzzz sir 🙏🏻

[@YashiSharma-sl2lw]

Last answer of function is R={-5,5}

[@gamerarceus1787]

sir, answer of question 2 is wrong i.e. 56. It should be 52 because blue and green balls are not 12 so we cannot blindly apply pegion hole principle.

[@bhiseahilya3632]

Sir f: Z to Z is not one one function. for f(x)=x^2..i think 🤔

[@MahimaPattanayak-il6pg]

Sir can you please provide your lecture notes pdf or ppt of all videos of discrete mathematics???

[@AbdulNaveed-e6g]

B is the domain❤❤❤

[@sabyasachhi_2004]

Option B 20:05 I take 3 sec

[@deepshikhajaiswal1234]

Option c= R-{5}

[@IncredibleEditz01]

B

[@exploringwithlakshbhai9755]

I think last question m range [-3,3] honi chahiye

[@creativething.]

option (b) is the correct answer

[@-KundanYadav]

Super sir 🔥

[@rohitpal8371]

Option C.( HW ans.)

[@raghuveersingh6323]

Please sir dynamics ke bhi videoes upload kijiye

[@career-for-student-life]

Sir las vale ka answer b , R/{5}

[@sanyachauhan5675]

Thankyou so much sirrr....🤍

[@esf1250]

Sir your are the best teacher 💫👌

[@Akash-k007]

Sir, please explain the theory of relativity... I looked out for it on yt, lekin agar aap explain karoge to jyada easy rahega..

[@ganeshsaha4136]

@VigyanRecharge

[@chandankumargupta8174]

B is right answer sir

[@anshulkshirsagar8200]

20:00 R{-5} and it took e 3 minutes sir

[@anshulkshirsagar8200]

no, its R/{5}😅

[@puneetbansal3042]

Answer B 5sec

[@tanvirhossainreza735]

explain slowly deeply and in details

[@officialvijaydangi5563]

Sir question no.3 ka (b) wrong he uska range [0,3] hi aayega

[@shubhamssoni4729]

i take 10 sec for last question corect option is B

[@currentelectric7764]

Option (B) R/{5}

[@souvikdutta3567]

Sir, up gate cse ke liye ek questions answers ka practice book nikal sakte jaha per pyqs nehi rahega

[@AK67-l1u]

Sir I am from west bengal Sir I take jam coaching from you 2023,,, When will the class start 2023?

[@moh1tg]

3rd question mai range [0,3] hi hoga

[@RoyaIfamily-q4t]

Only 2 sec answer [R\5]

[@hritiksharma1881]

OPTION (B) 15SEC

[@theinnovativenerd]

option B time taken = 1s

[@currentelectric7764]

Range is R -{0}

[@nitinswami7541]

Ans. B time takes 15sec

[@SachinPilotFanClub_]

Domain is R-{5} and range is R-{0}

[@Itz_sheev]

Sir inn ki pdf kahan milegi??

[@jyotishrimali701]

R/5