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Re: QOTD#11 Which of the following functions f defined for all n [#permalink]
23 Aug 2016, 13:56

2

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Expert's post

Explanation

If 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

Re: QOTD#11 Which of the following functions f defined for all n [#permalink]
10 Sep 2017, 09:07

1

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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.

Re: QOTD#11 Which of the following functions f defined for all n [#permalink]
10 May 2018, 12:20

Expert's post

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]
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.

greprepclubot

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