It is currently 18 Nov 2018, 14:36
My Tests

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

QOTD#11 Which of the following functions f defined for all n

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4711
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1614 [0], given: 376

CAT Tests
QOTD#11 Which of the following functions f defined for all n [#permalink] New post 19 Aug 2016, 05:19
Expert's post
00:00

Question Stats:

82% (00:53) correct 17% (01:37) wrong based on 28 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
[Reveal] Spoiler: OA

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4711
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1614 [0], given: 376

CAT Tests
Re: QOTD#11 Which of the following functions f defined for all n [#permalink] New post 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,

f(x) = \(\frac{x^3}{(x^2 +1)}\) or

f(-x)= \(\frac{(-x)^3}{((-x)^2 +1)}\) = \(\frac{- x^3}{(x^2 +1)}\) = -f(x).

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.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

1 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 1177
Followers: 44

Kudos [?]: 1054 [1] , given: 6

CAT Tests
Re: QOTD#11 Which of the following functions f defined for all n [#permalink] New post 23 Aug 2016, 13:56
1
This post received
KUDOS
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
[Reveal] Spoiler:
A


RELATED VIDEO

_________________

Brent Hanneson – Creator of greenlighttestprep.com
Image
Sign up for our free GRE Question of the Day emails

Intern
Intern
Joined: 18 Aug 2017
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 2

Re: QOTD#11 Which of the following functions f defined for all n [#permalink] New post 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.
Intern
Intern
Joined: 17 Mar 2018
Posts: 9
Followers: 0

Kudos [?]: 2 [0], given: 7

Re: QOTD#11 Which of the following functions f defined for all n [#permalink] New post 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
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4711
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1614 [0], given: 376

CAT Tests
Re: QOTD#11 Which of the following functions f defined for all n [#permalink] New post 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.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Intern
Intern
Joined: 19 Jun 2018
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: QOTD#11 Which of the following functions f defined for all n [#permalink] New post 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?
1 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 1177
Followers: 44

Kudos [?]: 1054 [1] , given: 6

CAT Tests
Re: QOTD#11 Which of the following functions f defined for all n [#permalink] New post 19 Jun 2018, 07:07
1
This post received
KUDOS
Expert's post
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

So, (-x)² + 1 = x² + 1

Does that help?

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
Image
Sign up for our free GRE Question of the Day emails

Re: QOTD#11 Which of the following functions f defined for all n   [#permalink] 19 Jun 2018, 07:07
Display posts from previous: Sort by

QOTD#11 Which of the following functions f defined for all n

  Question banks Downloads My Bookmarks Reviews Important topics  


GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.