Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 01 Jul 2015, 17:29

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

Author Message
Manager
Joined: 29 Oct 2009
Posts: 211
GMAT 1: 750 Q50 V42
Followers: 78

Kudos [?]: 857 [0], given: 18

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

?

_________________
Attachments

1.gif [ 13.34 KiB | Viewed 921 times ]

_________________

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

1) Translating the English to Math : word-problems-made-easy-87346.html

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1161
Followers: 302

Kudos [?]: 952 [1] , given: 4

1
KUDOS
Expert's post
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.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Manager
Joined: 29 Oct 2009
Posts: 211
GMAT 1: 750 Q50 V42
Followers: 78

Kudos [?]: 857 [0], given: 18

Thanks so much Ian.

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

Cheers.
_________________

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

1) Translating the English to Math : word-problems-made-easy-87346.html

Intern
Joined: 03 Nov 2010
Posts: 13
Followers: 0

Kudos [?]: 0 [0], given: 0

Would someone be able to explain why b is the answer?
I'm really not sure how to approach this problem...
Math Expert
Joined: 02 Sep 2009
Posts: 28227
Followers: 4460

Kudos [?]: 44965 [0], given: 6637

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.

_________________
Intern
Joined: 03 Nov 2010
Posts: 13
Followers: 0

Kudos [?]: 0 [0], given: 0

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"?
Math Expert
Joined: 02 Sep 2009
Posts: 28227
Followers: 4460

Kudos [?]: 44965 [0], given: 6637

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 $$f(9)=f(9^2)=f(81)$$.
_________________
Similar topics Replies Last post
Similar
Topics:
M05-05: Function 0 28 Jul 2013, 21:12
Question about functions 1 05 May 2013, 06:58
Functions 1 10 Dec 2009, 16:11
M21 Ques36 Doubt 1 30 Nov 2009, 18:48
maths 08 question #4 doubt 1 28 Oct 2009, 09:06
Display posts from previous: Sort by

Moderators: Bunuel, WoundedTiger

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.