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doubt about functions...

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doubt about functions... [#permalink] New post 18 Nov 2009, 09:07
I have a doubt.. suppose we were to write all of them in the form of functions of x,

for eg:

1) f(x^2) = f(x)*f(x)

2) f(x) = f(x^4)

3) f(x) = -f(x^2)

then would choices 4 and five be :

4) f(x) = 3*f(x)

5) f(x) = 0

or

4) f(x) = x*f(x)

5 f(x) = x

?

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Re: doubt about functions... [#permalink] New post 20 Nov 2009, 09:59
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sriharimurthy wrote:
I have a doubt.. suppose we were to write all of them in the form of functions of x, then would choices 4 and five be :

4) f(x) = 3*f(x)

5) f(x) = 0

or

4) f(x) = x*f(x)

5 f(x) = x


You cannot rewrite each answer as a function of x. If I tell you, for example, that f(2) = 2, there are infinitely many possible functions for f(x). It might be that f(x) = x, or that f(x) = 2, or that f(x) = x^2 - 2, or that f(x) = 17x - 32, or that f(x) = 3^x - 7, to give a few examples. When you are told about a specific value of a function -- for example, if you're told that f(5) = 10 -- that only gives you a single point on the graph of y = f(x) (all you know is that the graph contains the point (5,10)). It gives you no information at all about the rest of the graph, and therefore gives very little information about the definition of the function. So in the attached question, you will not be able to determine what f(x) is from any of the answer choices. Instead you need to use the property given -- that f(x) = f(x^2) -- to see which answer choice can be proven to be true. If f(x) = f(x^2), then f(-2) = f(4), and applying this again, f(4) = f(16), which makes B the correct answer. We still don't know what f(x) is, however.
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Re: doubt about functions... [#permalink] New post 20 Nov 2009, 10:11
Thanks so much Ian.

I've waited a long time for someone to clear this doubt of mine.

Cheers.
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Click below to check out some great tips and tricks to help you deal with problems on Remainders!
compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942

Word Problems Made Easy!
1) Translating the English to Math : word-problems-made-easy-87346.html
2) 'Work' Problems Made Easy : work-word-problems-made-easy-87357.html
3) 'Distance/Speed/Time' Word Problems Made Easy : distance-speed-time-word-problems-made-easy-87481.html

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Re: doubt about functions... [#permalink] New post 06 Apr 2012, 12:04
Would someone be able to explain why b is the answer?
I'm really not sure how to approach this problem...
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Re: doubt about functions... [#permalink] New post 06 Apr 2012, 12:25
Expert's post
KGG88 wrote:
Would someone be able to explain why b is the answer?
I'm really not sure how to approach this problem...


If function \(f(x)\) satisfies \(f(x) = f(x^2)\) for all \(x\), which of the following must be true?
A. \(f(4) = f(2)f(2)\)
B. \(f(16) - f(-2) = 0\)
C. \(f(-2) + f(4) = 0\)
D. \(f(3) = 3f(3)\)
E. \(f(0) = 0\)

We are told that some function \(f(x)\) has following property \(f(x) = f(x^2)\) for all values of \(x\). Note that we don't know the actual function, just this one property of it. For example for this function \(f(3)=f(3^2)\) --> \(f(3)=f(9)\), similarly: \(f(9)=f(81)\), so \(f(3)=f(9)=f(81)=...\).

Now, the question asks: which of the following MUST be true?

A. \(f(4)=f(2)*f(2)\): we know that \(f(2)=f(4)\), but it's not necessary \(f(2)=f(2)*f(2)\) to be true (it will be true if \(f(2)=1\) or \(f(2)=0\) but as we don't know the actual function we can not say for sure);

B. \(f(16) - f(-2) = 0\): again \(f(-2)=f(4) =f(16)=...\) so \(f(16)-f(-2)=f(16)-f(16)=0\) and thus this option is always true;

C. \(f(-2) + f(4) = 0\): \(f(-2)=f(4)\), but it's not necessary \(f(4) + f(4)=2f(4)=0\) to be true (it will be true only if \(f(4)=0\), but again we don't know that for sure);

D. \(f(3)=3*f(3)\): is \(3*f(3)-f(3)=0\)? is \(2*f(3)=0\)? is \(f(3)=0\)? As we don't know the actual function we can not say for sure;

E. \(f(0)=0\): And again as we don't know the actual function we can not say for sure.

Answer: B.
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Re: doubt about functions... [#permalink] New post 06 Apr 2012, 12:48
Bunuel wrote:
We are told that some function \(f(x)\) has following property \(f(x) = f(x^2)\) for all values of \(x\). Note that we don't know the actual function, just this one property of it. For example for this function \(f(3)=f(3^2)\) --> \(f(3)=f(9)\), similarly: \(f(9)=f(81)\), so \(f(3)=f(9)=f(81)=...\).


I believe it's the last part in bold that I don't get. How can F(3) = F(81)? F(3) = 9, F(9) = 81. Why is there a function before the "81"?
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Re: doubt about functions... [#permalink] New post 06 Apr 2012, 12:52
Expert's post
KGG88 wrote:
Bunuel wrote:
We are told that some function \(f(x)\) has following property \(f(x) = f(x^2)\) for all values of \(x\). Note that we don't know the actual function, just this one property of it. For example for this function \(f(3)=f(3^2)\) --> \(f(3)=f(9)\), similarly: \(f(9)=f(81)\), so \(f(3)=f(9)=f(81)=...\).


I believe it's the last part in bold that I don't get. How can F(3) = F(81)? F(3) = 9, F(9) = 81. Why is there a function before the "81"?


Given: \(f(x) = f(x^2)\) --> \(f(3)=f(3^2)=f(9)\) --> similarly \(f(9)=f(9^2)=f(81)\).
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: doubt about functions...   [#permalink] 06 Apr 2012, 12:52
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