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Please help me with this problem!

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Please help me with this problem!

by virtuoso902 » Wed Oct 07, 2009 11:16 am
Hey guys I tried searching around. I know this is a fairly straight forward problem but I have spent way too much time on it.

Thanks guys!

For which of the following functions f is f(x)=f(1-x) for all x?

A) f(x)=1-x
B) f(x)=1-x^2
C) f(x)=x^2-(1-x)^2
D) f(x)=x^2(1-x)^2
E) f(x)=x/(1-x)

[spoiler]
The Answer is D[/spoiler]
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by xcusemeplz2009 » Wed Oct 07, 2009 11:23 am
D is correct

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

hence f(x)=f(1-X)

basically we need to substitute 1-x for x in the eqn and check the value if it is same as of fx then its correct
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by Katrusya » Wed Oct 07, 2009 11:27 am
Why don't you insert in each of these options (1-x) instead of x and then you'll see.
It's really easy.
For example, let's take B
f(x)=1-x^2
f(1-x) = 1-(1-x)^2=1-1+2x-x^2= 2x-x^2
Hence, f(1-x)doesn't equal f(x)

Following this rule - you'll see D is right
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by virtuoso902 » Wed Oct 07, 2009 11:37 am
Thank you guys for your quick replies. You have helped me out a lot.
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by virtuoso902 » Wed Oct 07, 2009 11:43 am
Is there a faster way to get the answer instead of just plug 1-x into each of the answer choices?


Thank you!
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by xcusemeplz2009 » Wed Oct 07, 2009 11:57 am
virtuoso902 wrote:Is there a faster way to get the answer instead of just plug 1-x into each of the answer choices?


Thank you!
we can also use some simple values like x=1
and then check each option
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by glorydefined » Wed Oct 07, 2009 12:17 pm
ofcourse, substitute values, take x=2 then f(x)=2 and f(1-x)=-1

check for all given conditions and only option D satisfies it :

f(2)=x^2(1-x)^2 = 4(1-2)^2 = 4
f(-1)= (-1)^2 * (1+1)^2 = 4

:)
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by virtuoso902 » Thu Oct 08, 2009 8:49 am
Thank you guys for your very helpful replies.

I've gathered that this is probably the fastest way to do this problem. Let me know if I am wrong.

I will take 2 substitute it for X and just plugging it into all of the answer choices.

Is this the fastest way? Should i start with answer choice C and move down or just go down the list?

Thank you!
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