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

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Math Expert
Joined: 02 Sep 2009
Posts: 48067
Which of the following functions f has the property that f(−x)=−f(x) f  [#permalink]

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20 Feb 2017, 02:09
00:00

Difficulty:

55% (hard)

Question Stats:

63% (01:07) correct 37% (03:16) wrong based on 98 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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Which of the following functions f has the property that f(−x)=−f(x) f  [#permalink]

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20 Feb 2017, 02:41
3
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]

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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]

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13 Apr 2017, 09:09
Bunuel
Please explain this I am unable to understand
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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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13 Apr 2017, 09:42
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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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23 Jul 2018, 10:27
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Re: Which of the following functions f has the property that f(−x)=−f(x) f &nbs [#permalink] 23 Jul 2018, 10:27
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