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

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

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New post 20 Feb 2017, 01:09
1
8
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

63% (01:36) correct 38% (01:30) wrong based on 109 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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New post 20 Feb 2017, 01:41
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
Hit Kudos if you liked it 8-)
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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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New post 20 Feb 2017, 17:01
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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New post 13 Apr 2017, 08:09
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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New post 13 Apr 2017, 08:42
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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http://gmatclub.com/forum/let-the-funct ... 43311.html
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https://gmatclub.com/forum/which-of-the ... 01463.html
https://gmatclub.com/forum/for-which-of ... 88419.html

Hope it helps.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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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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New post 23 Jul 2018, 09:27
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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, 09:27
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