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QOTD#11 Which of the following functions f defined for all n [#permalink]
19 Aug 2016, 05:19
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34% (01:20) wrong based on 144 sessions
Which of the following functions f defined for all numbers x has the property that \(f(–x) = –f (x)\) for all numbers x ? A. f(x)= \(\frac{x^3}{(x^2 +1)}\) B. f(x)= \(\frac{(x^2  1)}{(x^2 + 1)}\) C. f(x)= \(x^2(x^2  1)\) D. f(x) = \(x(x^3  1)\) E. f(x) = \(x^2(x^3  1)\) Practice Questions Question: 13 Page: 152
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Re: QOTD#11 Which of the following functions f defined for all n [#permalink]
23 Aug 2016, 13:56
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ExplanationIf f(–x) = –f(x) for all numbers x, then let's see what happens with some arbitrary value of x. Let x = 2. The correct answer will be such that f(2) = f(2)A) f(2) = 8/5 and f(2) = (8/5) = 8/5. In this case, f(–x) = –f(x) . KEEP B) f(2) = 3/5 and f(2) = (3/5) = 3/5. In this case, f(–x) ≠ –f(x) . ELIMINATE C) f(2) = 12 and f(2) = (12) = 12. In this case, f(–x) ≠ –f(x) . ELIMINATE D) f(2) = 18 and f(2) = (14) = 14. In this case, f(–x) ≠ –f(x) . ELIMINATE E) f(2) = 36 and f(2) = (28) = 28. In this case, f(–x) ≠ –f(x) . ELIMINATE By the process of elimination, the correct answer is A Cheers, Brent
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Re: QOTD#11 Which of the following functions f defined for all n [#permalink]
10 Sep 2017, 09:07
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I think the question has not enough conditions to make Choice A unique. It assumes with all values of x, so what happens if x=0, if so, all Choices A, C, D, & E are correct.



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Re: QOTD#11 Which of the following functions f defined for all n [#permalink]
09 May 2018, 23:35
I think I'm a little confused with f(x).
For instance, if f(x) = x+1, then does f(x) = (x+1) or x+1



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Re: QOTD#11 Which of the following functions f defined for all n [#permalink]
10 May 2018, 12:20
jen6 wrote: I think I'm a little confused with f(x).
For instance, if f(x) = x+1, then does f(x) = (x+1) or x+1 If \(f(x) = x+1\) then \(f(x) = 1 \times (x+1)\) and \(f(x) = (x+1)\). If \(f\) is multiplied with 1 then everything gets multiplied with 1 if only x (variable) is multiplied with 1 then only variable terms get multiplied with 1.
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Re: QOTD#11 Which of the following functions f defined for all n [#permalink]
19 Jun 2018, 06:40
This may seem like a silly question, but how does (x)^2+1 become x^2+1 in the denominator? What happens to the negative sign?



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Re: QOTD#11 Which of the following functions f defined for all n [#permalink]
19 Jun 2018, 07:07
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rnmcdaniel wrote: This may seem like a silly question, but how does (x)² + 1 become x² + 1 in the denominator? What happens to the negative sign? Good question. Let's think of x as (1)(x) So, (x)² = [(1)(x)]² = [(1)(x)][(1)(x)] = (1)(1)(x)(x)= (1)x²= x² So, (x)² + 1 = x² + 1 Does that help? Cheers, Brent
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Re: QOTD#11 Which of the following functions f defined for all n [#permalink]
14 Feb 2019, 01:21
dzungpham wrote: I think the question has not enough conditions to make Choice A unique. It assumes with all values of x, so what happens if x=0, if so, all Choices A, C, D, & E are correct. That is the thing!! You see Choices A, C, D, & E are correct for only x = 0, and in some cases x=1 but not for all values of x. For example, if x = 2, then for choice B: f(x) = 1/3 and f(x) = (1/3) The only answer choice that fulfills the given condition for all values of x is only choice A.




Re: QOTD#11 Which of the following functions f defined for all n
[#permalink]
14 Feb 2019, 01:21





