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Functionsby Total Gadha - Thursday, 2 July 2009, 10:33 AM

In a CAT classroom or on the internet, there are two kinds of students- those who study and those who believe that they are studying but are actually not. Every time I start taking a fresh batch, it hardlytakes one or two classes to identify both types of students. And it has nothing to do with intelligence or background. It has to do with attitude and fighting spirit. Every time I throw a problem in the class orpost it in the forums, the students who are studying would be trying hard to solve the problem. They would arrive at an answer, whether right or wrong. On the other hand, the students are who are just‘striking a pose of studying’ would be waiting for me to give the answers and the solutions. They would be acting as if they are thinking hard but in reality would not be thinking at all. On the internet, Ifrequently see students who waste time in idle chit chat when they should be busy solving problems. They feel satisfied that they have done ‘something’ for their CAT by looking at problem or talking aboutCAT to others but in essence they have done nothing and wasted one more day. “Students like these,” as I tell my serious students, “are going to fill up the CAT form to give you your 99 percentile.” Onething I have learnt from my past experiences is that you can never teach attitude to students. Either they have it or they don’t. Whereas winners focus on completing their tasks, whiners have excuses andways of work avoidance. In TathaGat, we have a strict rule for students to submit one book review per week. And sometimes we see the book review either copied from the net or written after hearing aboutthe content from their friends. We even have strict rule for submission of quant or DI assignments. And many students turn in their assignments half-attempted. The serious students, on the other hand,finish their assignments before time and would frequently come to me with “Sir aur material mil sakta hai kya?” There is a world of difference between the two attitudes. Where I constantly hear from thewhiners “Sir aap solve kar dijiye”, I also constantly hear from the winners “Sir abhi answer mat batayiye, solve karne dijiye.” The only sane advice for the instructors in this field, who sometimes feel asfrustrated as I do, is- spend 80% of your time with your winners. And winners are not the ones who score at the top. They are the ones who are fighting the hardest, whether they are weak or strong inthe subject does not matter. And for students on the internet who want to do idle chit chat in the forums or engage in socializing, you would find TotalGadha.com too boring a place. We are serious aboutstudies here.

For our students on TG.com, we would like to share one of our endeavors in CAT CBT Club- Video lessons. Dagny and I have been tinkering with our camera and trying to make some good video lessons for our CBT Club students. We have uploadedone such video- Divisors of a number- for our TG junta. Do have a look and give us your feedback. Unfortunately, to watch the rest of the lessons that we are making, you will have to become a member of our exclusive club.

mba, cat, gmat, cat 2009, cat 2010, online cat 2009, 2010, cat preparation, gmat preparation, gmat verbal, cat results, cat papers, gmat score, cat co... http://totalgadha.com/mod/forum/discuss.php?d=5440

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Ratings: 5 / 5 (4)

Re: Functionsby Rohit Ghosh - Thursday, 2 July 2009, 01:31 PM

Nice article TG, as usual supreme quality.

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Ratings: 4 / 5

Re: Functionsby abhik chakraborty - Thursday, 2 July 2009, 04:12 PM

tg sir,i am puzzled of what category i am till now. but one thing i know for sure what i should try to be or at least try to do. and the article on function is incredible.thank you.

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Re: Functionsby Total Gadha - Thursday, 2 July 2009, 04:38 PM

Hi Abhik,

I really do not know about that but I think you (and everyone else) should read this-

http://totalgadha.com/tgtown/amitkumar/2009/05/16/are-u-really-preparing/

Total Gadha

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Re: Functionsby Veena Binya - Thursday, 2 July 2009, 04:35 PM

Hi TG..

The range of the function 1/1+root(x) has been given as [0,1]

Should it not be (0,1] ?Because it can only tend to 0, but can never become 0....

RegardsVeena

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Re: Functionsby Nikhil Rajagopalan - Thursday, 2 July 2009, 06:00 PM


5 of 9 7/23/2009 12:00 AM

nice one

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Re: Functionsby Swat cat - Thursday, 2 July 2009, 06:24 PM

Lesson is as usual excellent.

But the sentence that stole the show is

“Students like these,” as I tell my serious students, “are going to fill up the CAT form to give you your 99 percentile.”

A wake-up call .

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Re: Functionsby SHEKHAR SHARMA - Thursday, 2 July 2009, 07:56 PM

hi tg sir......

really this article abt to know urself that in which catagory i am, is really inspirable.........n also basic knowledge abt function is very good.

thank you sir

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Re: Functionsby Harshit @IIM - Friday, 3 July 2009, 02:07 PM

Awesome article as usual but i dont know when to calculate f(x+1) and when to f(1-x) or f(x-1) so as to get a relation between two sequence.

for example in question

f(1)=3600 and f(1) + f(2) + ....f(n)=n^2f(n)

u have calculated f(n+1) to simplify but in question

f(x)=9^x/(9^x + 3)

u have calculated f(1-x).

I guess this decision comes with practise but still i want to ask you any tips on how to decide which value to calculate.

Please suggest

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Re: Functionsby ayush roy - Friday, 3 July 2009, 03:56 PM

sir

it is a vry nice article....

sir m an engineering student,have passed out this year only,a vry serious follower of this site,n a big fan of ur articles.....wen i was preparin for IIT JEE,the most serious prb which i was facin was to sketch the graphs, i always wanted to do that,coz it helped a lot in physics also.sir what ever u hav explained ovr here is abt analyzin a function,which m vry gud at,but it has nvr helpd me in sketchin d graphs....i was nvr able to correlate both analyzin and sketchin.plz tell me how i can do that vry easily,without puttin values into a function.

thank you

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Re: Functionsby shiva chepuri - Friday, 3 July 2009, 06:58 PM

it is a wonderful article !!!

please discuss types of function if possible

sir

Sqrt(4-x2)

range should be (-infinity , 2]

because sqrt(x) outcome is R

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Doubt In Functionsby A B C - Saturday, 4 July 2009, 01:43 PM

HI TG...

I have a doubt here..

f(x) = odd and g(x) = even then f(g(x)) = odd..

now consider f(x) = x^3 and g(x) = x^2 than

f(g(x)) = x^6..which is an even function and hence contradicts

the statement...

Am i missing some concept here ..?

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Re: Functionsby Total Gadha - Saturday, 4 July 2009, 06:18 PM

Hi Shiva,

Give me one example when it is more than 2.

Total Gadha

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Re: Doubt In Functionsby Total Gadha - Saturday, 4 July 2009, 06:20 PM

Hi Shailendra,

I don't see the statement you have mentioned. The case you are mentioning, I have specified that it is an even function. Where is the contradiction?

Total Gadha

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Ratings: 5 / 5

Re: Doubt In Functionsby manjushaa srinivasan - Saturday, 4 July 2009, 11:02 PM


6 of 9 7/23/2009 12:00 AM

Hi TGi found your article very thought-provoking and clear cut.Himanshu's blog was also very inspirational.In my opinion any serious CAT aspirant who reads your article would become more dedicated towards his/her CAT preparation.Your explanation of functions was also veryuseful.I just want 1 advice from you.I'm not natural with quant.Even though i've been practising all along,i'm not sure if i can think as analytically as most of the other aspirants who are strong in quant .so far i've tried to cover all chapters but i would like to know if i'd be able tocrack the quant section if i'm well versed with number system,geometry,averages,percentages,alligations,profit and loss,interest,functions,set theory,progressions,probability,logarithms,surds and indices.although i'm practising problems from P&C,Mensuration but i get stuckwhen the sum is slightly twisted.this is worrying me.Regardsmanjushaa

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Re: Doubt In Functionsby manjushaa srinivasan - Saturday, 4 July 2009, 11:05 PM

I also have a problem visualising 3 D figures especially cubes which is hampering my speed and accuracy in mensuration to a great extent.What exactly should i do about this?

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Re: Functionsby Mohit Sharma - Sunday, 5 July 2009, 01:40 AM

Nice Article...Tg

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Re: Doubt In Functionsby Total Gadha - Sunday, 5 July 2009, 04:31 AM

Hi Manjusha,

The trick to get good at quant is to try and solve a lot of problems on your own. Try to solve them in any which manner that you can- by putting values, by generalizing, by longer methods or by using

theorems etc. But solve as much as you can. You will get good at this as you go along.

Total Gadha

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Re: Doubt In Functionsby Veena Binya - Sunday, 5 July 2009, 09:46 AM

Hi TG..

The range of the function 1/1+root(x) has been given as [0,1]

Should it not be (0,1] ?Because it can only tend to 0, but can never become 0....

RegardsVeena

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Re: Doubt In Functionsby manjushaa srinivasan - Sunday, 5 July 2009, 02:34 PM

hi TGThanks for the reply.previously when cat was CBT,it was feasible to leave few tough topics like P&C,inequalities,TSD etc if we were strong with number system,geometry,P&L,percentages,functions,averages,alligations,progressions,log,algebra.With the new pattern do we have cover the entiresyllabus?how is it possible to solve DI directly from computer screen especially the ones which involve tables where we need to calculate and give rankings etc?Since skimming and scanning of RCs,skillful selection of sitter questions are redundant now,what should be our newstrategy?

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Re: Doubt In Functionsby amit jain - Monday, 6 July 2009, 10:45 PM

can some one explain the question, area between the coordinate axis and fff(x). I am nt getting it.

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Re: Functionsby Prakash jain - Wednesday, 8 July 2009, 07:48 AM

sir you have realy openend my eyes, i belong to the 1st category, i have been pretending to prepare for CAT since 2 year but today i have realised that my previous efforts were not true, now I promise you that i will seriously prepare for this exam,and will perform well,thankyou so much for such a wonderful article...

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Re: Functionsby Dipanjan Biswas - Wednesday, 8 July 2009, 12:18 PM

At first I want to give you thanks for writing such a helluva article..It helped me to find my loopholes regarding one of the most important sections of quant.I would like to draw your attention on a few typo errors..(1)How to draw a graph of F(x): Point number three..Latter one should be for maximum..(2)f(x)=x^3(x+2) the second derivative of this function is positive..

Sir,I find it hard to draw any rectangular hyperbola graph..Can you elucidate it further..

TG Rockzzz\m/

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Re: Functionsby dishant dhokia - Thursday, 9 July 2009, 11:58 AM

For how many values of x is f(f(f(x))) = 19?

In this sum

f(f(f(x))) = 19

The next step is f(f(x)) = 38………….

I am not able to deduce this………..

Please someone elaborate???????????

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Re: Functionsby Dipanjan Biswas - Friday, 10 July 2009, 08:21 AM

Hi Dishant,Look at the function..See f(x) = x/2 if x is even = x+1 if x is oddIn other wayx=2f(x) if f(x) is either even or oddx=f(x)-1 if f(x) is evenAs f(x)=19=oddso x=38likewise f(x)=38x=76 or 37likewise f(x)=76x=152 or 75for f(x)=37x=74so {x}=>{74,75,152}


7 of 9 7/23/2009 12:00 AM

Hope it helps

Cheers!!

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Got a doubtby Varun Agrawal - Friday, 10 July 2009, 03:01 PM

Please discuss types of function if possible

sir

Sqrt(4-x2)

range should be [-2 , 2]

because sqrt(x) of a number gives 2 values. Positive and negative. Can you please elucidate how it is [0,2]

Thanks

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Re: Got a doubtby Dipanjan Biswas - Saturday, 11 July 2009, 01:38 PM

Varun please do go back to the question..It does not want the range of x rather the range of f(x).Max of f(x)=2 when x=0Min of f(x)=0 when x=+-2So f(x) [0,2]Please don't be in haste before raising your doubts. TG family takes utmost care before publishing these lessons..

Hope you have accepted my comment on a positive note!!All the best!!

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Re: Functionsby shiva chepuri - Saturday, 11 July 2009, 08:00 PM

yes sir

got it

but it should be [-2,2]

if i am wrong

plz correct

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Re: Functionsby Varun Goenka - Sunday, 12 July 2009, 10:22 PM

the func. is basically y=sqrt(4-x^2)

i.e. y^2=4-x^2

this is equation of a circle...x^2 + y^2 = 4...with origin as centre and 2 as radius...

but the given f(x) is just the upper half of the circle..

y=sqrt(4 - x^2)...is for upper half of the circle...

y= -sqrt(4 - x^2)...is for lower half of the circle...

our question is related to upper half of the circle...so range is [0,2] and domain is [-2,2]..

I think this should help...

Regards,

Varun Goenka

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Re: Functionsby Siddharth sahoo - Monday, 13 July 2009, 03:36 PM

@sahil, As discussed by you, x^2 * x^3 will be x^5. X^m * x^n = x(m+n).x5 is an odd function.

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Re: Doubt In Functionsby soumen paul - Tuesday, 14 July 2009, 06:59 PM

f(x)=x^3 is not a odd function if x=2,4,6........

g(x)=x^2 is not a even function if x=3,5,7........

f(x)=2x+1 is a odd function for 0,1,2.....

g(x)=2x+2 is a even function for 0,1,2......

so here f[g(x)]=4x+5 is a odd function

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Re: Functionsby Ashish Kumar - Thursday, 16 July 2009, 12:23 AM

lol PATAKKA article....but what i loved more is those who are whiners and are reading this can actually do something still coz there is still time but even after this if they cannot do anything then trust me they are helping the winners more n more lol ROFL !!!

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Re: Functionsby Abhishek Samanta - Thursday, 16 July 2009, 04:19 AM

Hi TG,

Simply superb article...I think I have fallen in love with functions...can you please add more problems on functions? or may be one set of problems? or may be some book....anything will do....

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Re: Functionsby Abhishek Samanta - Thursday, 16 July 2009, 04:24 AM

hi dishant,

take it this way...can f(x) ever be odd?

when x is odd, f(x)=x+1...so it will always give you even f(x)..

when x is even, f(x)=x/2; this is only chance when you can get odd f(x)..

here f(m) [m=f(f(x)) ] is odd.....so m must be even...

that means m/2=38

so, m=76 i.e. f(f(x))=76..


8 of 9 7/23/2009 12:00 AM

hope it helps

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Re: Functionsby piyush dixit - Friday, 17 July 2009, 09:39 PM

HI TG,I am a frequent reader of your post, and following this site almost since its inception. I am an adherent fan of yours, BUT I am very disappointed with this article of yours, and hence writing to you for the first time. I guess, you started this whole exercise of totalgadha.com toridicule the jargon taught by famous coaching classes in their curriculum to show their superiority among the students community, TG i belive you started the exercise to change the way education system works at this level. But it seems you are getting infected by the sameBUG.I am sorry, if i have misunderstood you.Hats off for all your other posts, which I have been through.

PIYUSH

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Ratings: 4 / 5

Re: Functionsby Total Gadha - Sunday, 19 July 2009, 10:49 PM

Hi Piyush,

I am infected by what I do, down to my last nail. My opinion should hardly matter to you. Take what is good and ignore everything else.

Total Gadha

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Ratings: 5 / 5 (2)

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