NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 18:24 It is currently 25 Apr 2024, 18:24
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If f(x)=x(1−x) for any x, then f(1−x) must be equal to which of the fo

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619033 [3]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
If f(x)=x(1−x) for any x, then f(1−x) must be equal to which of the fo [#permalink] New post   12 May 2021, 07:15
3
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

81% (00:50) correct 19% (01:56) wrong based on 69 sessions
Hide Show timer Statistics
If \(f(x)=x(1−x)\) for any x, then \(f(1−x\)) must be equal to which of the following?


A. x

B. f(x)

C. f(x−1)

D. x^2

E. 1−x
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619033 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: If f(x)=x(1−x) for any x, then f(1−x) must be equal to which of the fo [#permalink] New post   15 May 2021, 06:15
Expert Reply
Bunuel wrote:
If \(f(x)=x(1−x)\) for any x, then \(f(1−x\)) must be equal to which of the following?


A. x

B. f(x)

C. f(x−1)

D. x^2

E. 1−x


Since \(f(x)=x(1-x)\), then \(f(1-x) = (1-x)(1-(1-x))=(1-x)x\). We know that (1-x)x is f(x).

Answer: B.

Check functions related questions in our Special Questions Directory.

Operations/functions defining algebraic/arithmetic expressions
Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions
General Discussion
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5344
Own Kudos [?]: 3964 [0]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
If f(x)=x(1−x) for any x, then f(1−x) must be equal to which of the fo [#permalink] New post   12 May 2021, 08:41
Asked: If \(f(x)=x(1−x)\) for any x, then \(f(1−x\)) must be equal to which of the following?

\(f(1−x) = (1-x)(1-(1-x))= (1-x)x = f(x)\)

IMO B
User avatar
D
BrushMyQuant
Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1777
Own Kudos [?]: 2094 [1]
Given Kudos: 100
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Send PM
If f(x)=x(1x) for any x, then f(1x) must be equal to which of the fo [#permalink] New post   06 Dec 2023, 11:56
1
Kudos
Expert Reply
Top Contributor
f(x)=x(1−x)

Let's solve the problem using two methods:

Method 1: Symmetry

Since f(x) has same power of x and 1-x and both are in the numerator with the same sign
=> f(x) is symmetric with respect to x and 1-x
=> f(x) = f(1-x)

So, Answer will be B

Watch this video to learn about How to identify Symmetry in functions, this will help you save some good time in the test!

Method 2: Algebra

To find f(1-x) we need to compare what is inside the bracket in f(1-x) and f(x)
=> We need to replace x with 1-x in f(x)=x(1−x) to get the value of f(1-x)

=> f(1-x) = (1-x)*(1−(1-x)) = (1-x)*(1-1 + x) = (1-x)*x = f(x)

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

GMAT Club Bot
gmatclubot
If f(x)=x(1x) for any x, then f(1x) must be equal to which of the fo [#permalink]
06 Dec 2023, 11:56
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions