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# For which of following is f(-x) = -f(x)?

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Math Expert
Joined: 02 Sep 2009
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For which of following is f(-x) = -f(x)?  [#permalink]

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13 Mar 2019, 00:21
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Difficulty:

45% (medium)

Question Stats:

61% (01:26) correct 39% (01:05) wrong based on 33 sessions

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For which of following is $$f(-x) = -f(x)$$?

A. $$\frac{x^3}{x^2 + 1}$$

B. $$x^4 + x^2$$

C. $$x^2(x + x^2)$$

D. $$x^3(x^2 + x)$$

E. $$x^2(x^2 - x^)$$

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Re: For which of following is f(-x) = -f(x)?  [#permalink]

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13 Mar 2019, 04:14
Bunuel wrote:
For which of following is $$f(-x) = -f(x)$$?

A. $$\frac{x^3}{x^2 + 1}$$

B. $$x^4 + x^2$$

C. $$x^2(x + x^2)$$

D. $$x^3(x^2 + x)$$

E. $$x^2(x^2 - x^)$$

let x = 1
so at f(-1) = -f(x)
only valid at $$\frac{x^3}{x^2 + 1}$$

IMO A
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Re: For which of following is f(-x) = -f(x)?  [#permalink]

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16 Mar 2019, 13:28
1
Bunuel wrote:
For which of following is $$f(-x) = -f(x)$$?

A. $$\frac{x^3}{x^2 + 1}$$

B. $$x^4 + x^2$$

C. $$x^2(x + x^2)$$

D. $$x^3(x^2 + x)$$

E. $$x^2(x^2 - x^)$$

For answer choice A, (-x)^3 = -(x^3) and (-x)^2 + 1 = x^2 + 1. Thus, f(-x) = (-x)^3/[(-x)^2 + 1] = -(x^3)/(x^2 + 1) = -f(x). Thus, answer A is correct.

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Re: For which of following is f(-x) = -f(x)?  [#permalink]

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22 Mar 2019, 13:01
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Joined: 25 Feb 2019
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Re: For which of following is f(-x) = -f(x)?  [#permalink]

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22 Mar 2019, 18:48
arorni wrote:

Please put x = -x in given options

and check if you can find expression such that after taking -1 as common you find the same original expression.

Here A satisfy this condition .

then we say f(-x) = -f(x)

please try other options and see if you can take -1 common and find original expression

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Re: For which of following is f(-x) = -f(x)?   [#permalink] 22 Mar 2019, 18:48
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