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by msbelasco » Mon Aug 06, 2012 7:22 pm
For which of the following functions f is f(x) = f(x-1) for all x?

f(x) = 1-x

f(x) = 1-x^2

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

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

f(x) = x/1-x

I can not understand what the question is asking. Any help would be much appreciated.

Thanks
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by Anurag@Gurome » Mon Aug 06, 2012 7:43 pm
msbelasco wrote:For which of the following functions f is f(x) = f(x-1) for all x?

f(x) = 1-x

f(x) = 1-x^2

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

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

f(x) = x/1-x

I can not understand what the question is asking. Any help would be much appreciated.

Thanks

Let us look at each of the options:

(A) f(x) = 1-x
f(1-x) = 1 - (1-x) = x; FALSE

(B) f(x) = 1-x^2
f(1-x) = 1 - (1-x)^2 = 1 - (1 - 2x + x^2) = 2x - x^2; FALSE

(C) f(x) = x^2 - (1-x)^2
f(1-x) = (1-x)^2 - (1 - (1-x))^2 = 1 - 2x + x^2 - (x)^2 = 1 - 2x; FALSE

(D) f(x) = x^2 * (1-x)^2
f(1-x) = (1 - x)^2 * (1 - (1 - x))^2 = (1 - x)^2 * (x)^2; TRUE

(E) f(x) = x/(1-x)
so f(1-x) = (1-x)/(1-(1-x)) = (1-x)/x; FALSE

The correct answer is D.
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by msbelasco » Mon Aug 06, 2012 9:41 pm
Thanks for the reply, but it seems to me that you are plugging in f(1-x), instead of f(x-1). Am I missing something? Thanks
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by Anurag@Gurome » Mon Aug 06, 2012 10:01 pm
msbelasco wrote:Thanks for the reply, but it seems to me that you are plugging in f(1-x), instead of f(x-1). Am I missing something? Thanks
If I am not wrong, this question is from GMAT Prep, and there the correct questions is: For which of the following functions f is f(x) = f(1-x) for all x?

Please check the question again.
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by msbelasco » Tue Aug 07, 2012 1:53 am
You are certainly right. Thanks for your help!
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by GMATGuruNY » Tue Aug 07, 2012 2:51 am
msbelasco wrote:For which of the following functions f is f(x) = f(x-1) for all x?

f(x) = 1-x

f(x) = 1-x^2

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

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

f(x) = x/1-x

I can not understand what the question is asking. Any help would be much appreciated.

Thanks
Let x=2.
Then f(x) = f(2) and f(1-x) = f(1-2) = f(-1).
The question becomes:

For which of the following functions does f(2) = f(-1)?

Answer choice A:
f(2) = 1-2 = -1.
f(-1) = 1-(-1) = 2.
Doesn't work.

Answer choice B:
f(2) = 1 - 2^2 = -3.
f(-1) = 1 - (-1)^2 = 0.
Doesn't work.

Answer choice C:
f(2) = 2^2 - (1-2)^2 = 4 - 1 = 3.
f(-1) = (-1)^2 - [1-(-1)]^2 = 1-4 = -3.
Doesn't work.

Answer choice D:
f(2) = 2^2 * (1-2)^2 = 4 * 1 = 4.
f(-1) = (-1)^2 * [1-(-1)]^2 = 1 * 4 = 4.
Success!

Answer choice E:
f(2) = 2/(1-2) = -2.
f(-1) = (-1)/[(1-(-1)] = -1/2.
Doesn't work.

The correct answer is D.
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by Kobe_Kassidy » Thu Aug 09, 2012 1:33 pm
GMATGuruNY wrote:
msbelasco wrote:For which of the following functions f is f(x) = f(x-1) for all x?

f(x) = 1-x

f(x) = 1-x^2

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

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

f(x) = x/1-x

I can not understand what the question is asking. Any help would be much appreciated.

Thanks
Let x=2.
Then f(x) = f(2) and f(1-x) = f(1-2) = f(-1).
The question becomes:

For which of the following functions does f(2) = f(-1)?

Answer choice A:
f(2) = 1-2 = -1.
f(-1) = 1-(-1) = 2.
Doesn't work.

Answer choice B:
f(2) = 1 - 2^2 = -3.
f(-1) = 1 - (-1)^2 = 0.
Doesn't work.

Answer choice C:
f(2) = 2^2 - (1-2)^2 = 4 - 1 = 3.
f(-1) = (-1)^2 - [1-(-1)]^2 = 1-4 = -3.
Doesn't work.

Answer choice D:
f(2) = 2^2 * (1-2)^2 = 4 * 1 = 4.
f(-1) = (-1)^2 * [1-(-1)]^2 = 1 * 4 = 4.
Success!

Answer choice E:
f(2) = 2/(1-2) = -2.
f(-1) = (-1)/[(1-(-1)] = -1/2.
Doesn't work.

The correct answer is D.
So Mitch, did you use 2 for x for a particular reason, or can any arbitrary number be used in these types of problems?
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