GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 24 Apr 2019, 21:18

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.

Close

Request Expert Reply

Confirm Cancel

If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Intern
Intern
avatar
Joined: 08 Nov 2008
Posts: 27
If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1  [#permalink]

Show Tags

New post Updated on: 07 Mar 2017, 01:19
1
2
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

76% (01:21) correct 24% (02:15) wrong based on 163 sessions

HideShow timer Statistics

If f is the function defined by \(f(x) = x^2*(1-x)^2\) for all x, then f(1-x) =

A. f(x)
B. f(x)^2
C. 1 - f(x)
D. (1-x)*f(x)
E. f(1) - f(x)

Originally posted by petercao on 14 Nov 2008, 16:41.
Last edited by Bunuel on 07 Mar 2017, 01:19, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
VP
VP
User avatar
Joined: 05 Jul 2008
Posts: 1220
Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1  [#permalink]

Show Tags

New post 15 Nov 2008, 14:11
Just substitute (1-x) for x and you will see that f(1-x) is nothing but f(x)
Senior Manager
Senior Manager
avatar
Joined: 30 Aug 2009
Posts: 266
Location: India
Concentration: General Management
Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1  [#permalink]

Show Tags

New post 03 Sep 2011, 09:24
DeeptiM wrote:
If f is the function defined by f(x) = x^2 (1-x)^2 for all x, then f(1-x) =
A. f(x)
B. [f(x)]^2
C. 1 - f(x)
D. (1-x) f(x)
E. f(1) - f(x)



replace x by 1-x in the original expression and we would get f(1-x) = f(x)
Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1784
Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1  [#permalink]

Show Tags

New post 03 Sep 2011, 09:35
1
2
petercao wrote:
If f is the function defined by f(x) = x^2 (1-x)^2 for all x, then f(1-x) =

A. f(x)
B. [f(x)]^2
C. 1 - f(x)
D. (1-x) f(x)
E. f(1) - f(x)


\(f(x) = x^2 (1-x)^2\)

What is \(f(1-x)\)?

Just replace x with (1-x)
\(f(1-x) = (1-x)^2 (1-(1-x))^2\)
\(f(1-x) = (1-x)^2 (x)^2\)
\(f(1-x) = (x)^2(1-x)^2 = f(x)\)

Ans: "A"
********************************

Or pick x=3; 1-x=1-3=-2
\(f(1-x)=f(-2)=(-2)^2*(1-(-2))^2=4*9=36\)

Let's check each option separately:

A. f(x)
\(f(3)=3^2*(1-3)^2=9*4=36\). Holds good. Possible answer.

B. [f(x)]^2
\((36)^2\). Ignore

C. 1 - f(x)
\(1-36=-35\). Ignore

D. (1-x) f(x)
\((1-3)(36)=36*-2=-72\). Ignore

E. f(1) - f(x)
\(1^2*(1-1)^2-36=0-36=-36\). Ignore.

Only A gave us what we got with f(1-x) i.e. f(-2).

Ans: "A"
_________________
Manager
Manager
avatar
Joined: 16 Feb 2011
Posts: 198
Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1  [#permalink]

Show Tags

New post 03 Sep 2011, 09:43
Thanks a lot fluke...i did the first way by replacing x with 1-x but then....god knows from where did i start converting the equation in (a+b)^2 form...silly me...

thanks again!!
Director
Director
avatar
Joined: 01 Feb 2011
Posts: 646
Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1  [#permalink]

Show Tags

New post 03 Sep 2011, 10:05
f(x) = x^2 * (1-x)^2

substituting x with 1-x , we should get f(1-x)

f(1-x) = (1-x)^2 * (1-(1-x))^2
= (1-x)^2 *x^2
= f(x)

Answer is A.
Senior CR Moderator
User avatar
V
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1354
Location: Viet Nam
GMAT ToolKit User
Re: If f is the function defined by f(x) = x^2 (1-x)^2  [#permalink]

Show Tags

New post 13 Aug 2017, 19:26
longhaul123 wrote:
If f is the function defined by f(x) = x^2 (1-x)^2 for all x, then f(1-x) =
A. f(x)
B. [f(x)]^2
C. 1 - f(x)
D. (1-x) f(x)
E. f(1) - f(x)

Can someone please help me with the method of substituting the numbers and finding out the answer for this question. Thank you


\(f(x)=x^2(1-x)^2 \implies f(1-x)=(1-x)^2(1-(1-x))^2=(1-x)^2x^2=f(x)\)

Answer A
_________________
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
Re: If f is the function defined by f(x) = x^2 (1-x)^2  [#permalink]

Show Tags

New post 13 Aug 2017, 19:45
longhaul123 wrote:
If f is the function defined by f(x) = x^2 (1-x)^2 for all x, then f(1-x) =
A. f(x)
B. [f(x)]^2
C. 1 - f(x)
D. (1-x) f(x)
E. f(1) - f(x)

Can someone please help me with the method of substituting the numbers and finding out the answer for this question. Thank you


Hi longhaul123,

Please find the method of number substitution

If x=2, f(x) = 4(1) = 4
So, f(1-x) = f(-1) = \(1(1 -(-1))^2 = 1(4) = 4\) = f(x) (Option A)

Hope that helps!
_________________
You've got what it takes, but it will take everything you've got
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54496
Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1  [#permalink]

Show Tags

New post 14 Aug 2017, 00:46
longhaul123 wrote:
If f is the function defined by f(x) = x^2 (1-x)^2 for all x, then f(1-x) =
A. f(x)
B. [f(x)]^2
C. 1 - f(x)
D. (1-x) f(x)
E. f(1) - f(x)

Can someone please help me with the method of substituting the numbers and finding out the answer for this question. Thank you


13. Functions



_________________
GMAT Club Bot
Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1   [#permalink] 14 Aug 2017, 00:46
Display posts from previous: Sort by

If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.