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

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Bunuel
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For which of following is f(-x) = -f(x)? [#permalink] New post   13 Mar 2019, 00:21
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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] New post   16 Mar 2019, 13:28
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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.

Answer: A
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Re: For which of following is f(-x) = -f(x)? [#permalink] New post   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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arorni
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Re: For which of following is f(-x) = -f(x)? [#permalink] New post   22 Mar 2019, 13:01
Can someone please help with this question in detail?
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Re: For which of following is f(-x) = -f(x)? [#permalink] New post   22 Mar 2019, 18:48
arorni wrote:
Can someone please help with this question in detail?



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



award kudos if helpful

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Re: For which of following is f(-x) = -f(x)? [#permalink] New post   29 Oct 2023, 08:00
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Re: For which of following is f(-x) = -f(x)? [#permalink]
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