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if function f(x) satisfies f(x)=f(x^2) for all x

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by bhumika.k.shah » Sun Jan 24, 2010 8:18 am
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)=f(0)

OA B

I used first value to find out its square and accordinly solved each option ...
i thought it was either A or E
but in reality it was B :(
just my luck! :-(
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by ajith » Sun Jan 24, 2010 8:41 am
bhumika.k.shah wrote: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)=f(0)
Check option E ( it says f(0) = f(0) which is an identity and hence should be true)

I can see why B is true

f(x)=f(x^2)

f(-2) = f(4)
f(4) = f (16)

hence f (16) - f (-2) = 0


As far as B goes

f(2) = f(2^2) = f(4)
f(4) = f (2) and not f(4) = f(2)*f(2)
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by bhumika.k.shah » Sun Jan 24, 2010 10:43 am
As far as B goes

f(2) = f(2^2) = f(4)
f(4) = f (2) and not f(4) = f(2)*f(2)[/quote]

I am sowree i dint understand this! r u talking about the correct option?
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by rahul.s » Sun Jan 24, 2010 10:44 am
i doubt whether such q's appear on the GMAT.
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by bhumika.k.shah » Sun Jan 24, 2010 10:45 am
wouldnt it be like f(16)= f(16^2) = 256
f(-2) = f(-2^2) = f4

therefore f(16)-f(-2) is not equal to zero and hence not true!

this is why i eliminated it ...

:-(
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by bhumika.k.shah » Sun Jan 24, 2010 10:47 am
There is no limit to possibilities :-)
rahul.s wrote:i doubt whether such q's appear on the GMAT.
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by ajith » Sun Jan 24, 2010 10:54 am
bhumika.k.shah wrote:wouldnt it be like f(16)= f(16^2) = 256
f(-2) = f(-2^2) = f4

therefore f(16)-f(-2) is not equal to zero and hence not true!

this is why i eliminated it ...

:-(
Well a function can be anything to evaluate it you need a formula

For example f(x) = x^2+x+1 is a function

and if that is the function f(2) = 2^2+2+1 = 7

In this case,

all that is given is f(x) = f (x^2)

You are saying, f(16)= f(16^2) which is right but it f(256) is not equal to 256 and we have not given information to calculate the function

Further = f(-2) = f(4) = f(16) = f(256)

So, f(16) - f(-2) = 0

so is f(256) - f(16)
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by VikingWarrior » Sun Jan 24, 2010 11:01 am
wouldnt it be like f(16)= f(16^2) = 256
f(-2) = f(-2^2) = f4

therefore f(16)-f(-2) is not equal to zero and hence not true!

this is why i eliminated it ...
f(16) is not = 256
the function is not F(x)=x^2
This function to my limited knowledge can only lead to
1. f(0)=f(0)
2. f(1)=f(1)


Please correct me if I am wrong
Last edited by VikingWarrior on Sun Jan 24, 2010 12:20 pm, edited 1 time in total.
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by Brent@GMATPrepNow » Sun Jan 24, 2010 11:07 am
bhumika.k.shah wrote: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)=f(0)

OA B

I used first value to find out its square and accordinly solved each option ...
i thought it was either A or E
but in reality it was B :(
just my luck! :-(
How about if we try to find some function, f(x) such that f(x) = f(x^2)
This might help us eliminate some answer choices.

Here's a function that satisfies the initial requirement: f(x) = 3
So, f(2) = 3 and f(2^2)=3

If we use this function to check each answer choice, we can eliminate A, C and D.

At this point, we have to recognize that E must be true. We are saying some value (f(0))equals itself (f(0)). Hard to argue against that.

Also, ajith's explanation . . .
f(x)=f(x^2)
f(-2) = f(4)
f(4) = f (16)
Hence f (16) - f (-2) = 0
. . . demonstrates that B is also correct.

So, I'd say that we appear to have two correct answers (B and E)

What's the source?
Brent Hanneson - Creator of GMATPrepNow.com
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by bhumika.k.shah » Sun Jan 24, 2010 10:06 pm
gmat club tests

im finding this sum even more difficult now with all these various explanations... :(
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by ramanalokanathan » Wed Jan 05, 2011 11:58 pm
The original poster made a mistake when typing answer choice E, which should be:

f(0) = 0

( instead of f(0) = f(0) )

With this correction, Brent's explanation makes perfect sense.
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