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Re: QOTD#11 Which of the following functions f defined for all n [#permalink]
19 Aug 2016, 05:24

Expert's post

Explanation

To determine which of the functions among the five choices has the property that f (–x) =–f (x) for all numbers x, you need to check each choice until you find one that has the property. In Choice A,

Therefore Choice A has the property f (– x) = –f (x), and since only one of the five choices can be the correct answer, the correct answer is Choice A. _________________

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

1

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Expert's post

sandy wrote:

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

I prefer the solution that Sandy provided. However, here's a different approach.

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

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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