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Which of the following functions f has the property that f(−x)=−f(x) f

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Bunuel
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Which of the following functions f has the property that f(−x)=−f(x) f [#permalink] New post   20 Feb 2017, 02:09
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A
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E

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68% (01:48) correct 32% (01:41) wrong based on 216 sessions
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Which of the following functions f has the property that f(−x)=−f(x) for all numbers x?

A. (x^4−3)/(x^6+2)

B. −x^2/(x−1)^2

C. (x^3−7)/(x−2)^2

D. (x^4−x)/(x^2+2)

E. x^5/(x^2+4)
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E
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0akshay0
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Which of the following functions f has the property that f(−x)=−f(x) f [#permalink] New post   20 Feb 2017, 02:41
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Bunuel wrote:
Which of the following functions f has the property that f(−x)=−f(x) for all numbers x?

A. (x^4−3)/(x^6+2)

B. −x^2/(x−1)^2

C. (x^3−7)/(x−2)^2

D. (x^4−x)/(x^2+2)

E. x^5/(x^2+4)


f(−x)=−f(x)
f(−x) + f(x) = 0
Only \(x^5/(x^2+4)\) satisfies the above statement
\(x^5/(x^2+4)+ (-x)^5/((-x)^2+4) = x^5/(x^2+4)-x^5/(x^2+4) = 0\)

Hence Option E is correct
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Re: Which of the following functions f has the property that f(−x)=−f(x) f [#permalink] New post   20 Feb 2017, 18:01
Ok 2:49 I chose E- for example, first assume x= -2. Remembering f(-x) must = -f(x), then, plugging in -2 will yield exactly the same result.

-x^5/(x^2 + 4)

f(-x)
(-2)^5/(-2^2 + 4)
-32/(4+4)
-32/(8)
-4

-f(x)
(2)^5/((2)^2+4)
32/(4 +4)
32/(8)
-4
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Which of the following functions f has the property that f(−x)=−f(x) f [#permalink] New post   13 Apr 2017, 09:09
Bunuel
Please explain this I am unable to understand
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Bunuel
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Re: Which of the following functions f has the property that f(−x)=−f(x) f [#permalink] New post   13 Apr 2017, 09:42
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ehsan090 wrote:
Bunuel
Please explain this I am unable to understand


You can check detailed analysis of how to solve such question here: https://gmatclub.com/forum/for-which-of ... ml#p644387

After that you can practice similar questions:
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Hope it helps.
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Re: Which of the following functions f has the property that f(x)=f(x) f [#permalink] New post   09 Apr 2024, 03:07
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Re: Which of the following functions f has the property that f(x)=f(x) f [#permalink]
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