It is currently 19 Apr 2018, 20:01

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

For which of the following functions f is f(x) = f(1-x) for all x?

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44566
Re: For which of the following functions f is f(x) = f(1-x) for all x? [#permalink]

Show Tags

New post 27 Mar 2014, 10:47
rajatsp wrote:
Please do let me know if there are more similar questions besides the ones you mentioned.

Thank you

Rajat


Here are several more:
for-which-of-the-following-functions-does-f-x-f-2-x-155813.html
for-which-of-the-following-does-f-a-f-b-f-a-b-164979.html
for-which-of-the-following-functions-f-is-f-x-f-1-x-for-85751.html

Hope this helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Current Student
User avatar
Joined: 03 Aug 2011
Posts: 290
Concentration: Strategy, Finance
GMAT 1: 640 Q44 V34
GMAT 2: 700 Q42 V44
GMAT 3: 680 Q44 V39
GMAT 4: 740 Q49 V41
GPA: 3.7
WE: Project Management (Energy and Utilities)
GMAT ToolKit User Reviews Badge
Re: For which of the following functions f is f(x) = f(1-x) for all x? [#permalink]

Show Tags

New post 02 Sep 2014, 07:35
Bunuel, would you generally recommend picking numbers as a strategy for such questions (especially if the functions are for ALL X)? Or rather the algebraic approach?

Thanks!
_________________

Thank you very much for reading this post till the end! Kudos?

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44566
Re: For which of the following functions f is f(x) = f(1-x) for all x? [#permalink]

Show Tags

New post 02 Sep 2014, 08:13
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: For which of the following functions f is f(x) = f(1-x) for all x? [#permalink]

Show Tags

New post 03 Sep 2014, 01:14
VeritasPrepKarishma wrote:
metallicafan wrote:
Is there a faster way to solve this question rather than replacing each "x" by (1-x)? Thanks!

For which of the following functions \(f\) is \(f(x) = f(1-x)\) for all x?

A. \(f(x) = 1-x\)
B. \(f(x) = 1-x^2\)
C. \(f(x) = x^2 - (1-x)^2\)
D. \(f(x) = (x^2)(1-x)^2\)
E. \(f(x) = x / (1-x)\)


Tip: Try to first focus on the options where terms are added/multiplied rather than subtracted/divided. They are more symmetrical and a substitution may not change the expression. I will intuitively check D first since it involves multiplication of the terms.


Agreed; did in the same way :)

Option D returns the same term by substituting x with (1-x)

In the OA, had they expanded option D then calculation would be required

\(x^2 (1-x)^2 = [x(1-x)]^2 = (x - x^2)^2 = x^2 - 2x^3 + x^4\)

Now replacing x with (1-x) would had required serious calculation.....
_________________

Kindly press "+1 Kudos" to appreciate :)

Intern
Intern
avatar
Joined: 11 Oct 2013
Posts: 30
Re: For which of the following functions f is f(x) = f(1-x) for all x? [#permalink]

Show Tags

New post 15 May 2015, 08:46
I basically substituted and checked each option. Somehow I get this intuition that in such questions, one should actually start from option E and work backwards, rather than starting from option A and moving forward. The reason being that GMAT would not make it so easy that option A or B itself would satisfy:). Any observations? Has anyone come across such questions (on functions), where the correct answer is option A/B?

A. f(x) = 1 - x
=> f(1-x) = 1 - (1-x) = x

So, f(x) <> f(1-x)

B. f(x) = 1 - x^2
=> f(1-x) = 1 - (1-x)^2 = 1 - (1+x^2 - 2x) = 2x - x^2

So, f(x) <> f(1-x)

C. f(x) = x^2 - (1 - x)^2

=> f(1-x) = (1-x)^2 - [(1-(1-x)]^2 = (1-x)^2 - x^2

So, f(x) <> f(1-x)

D. f(x) = x^2*(1 - x)^2
=> f(1-x) = (1-x)^2 * [(1-(1-x)]^2 = (1-x)^2 * x^2

So, f(x) = f(1-x)

E. f(x) = x/(1 - x)
=> f(1-x) = (1-x)/[(1-(1-x)] = (1-x)/x

So, f(x) <> f(1-x)

Hence, D
Ryerson (Ted Rogers) Thread Master
User avatar
Joined: 27 Sep 2015
Posts: 57
Location: Canada
GMAT 1: 410 Q33 V13
WE: Management Consulting (Computer Software)
GMAT ToolKit User
Re: For which of the following functions f is f(x) = f(1-x) for all x? [#permalink]

Show Tags

New post 26 Dec 2015, 16:20
Big algebra is good but not prefer in these type if question. Plugin is best approach:

Assume x = 2.

\(f(2) = 2^2(1-2)^2\)
\(= 4(-1)^2 = 4*1= 4\)

\(f(1-2) or f(-1) = -1^2(1+1)^2\)
\(=1*2^2= 1*4=4\)

D is correct answer.
_________________

Discipline does not mean control. Discipline means having the sense to do exactly what is needed.

Manager
Manager
User avatar
Joined: 21 Jan 2014
Posts: 99
GMAT 1: 500 Q32 V28
GPA: 4
Re: For which of the following functions f is f(x) = f(1-x) for all x? [#permalink]

Show Tags

New post 11 Jan 2016, 14:21
Abhii46 wrote:
You need to check for every option.
Either you can replace x in every option with 1-x or you can take x = 1 and then check for which option f(1) = f(1-1) = f(0).
In A f(1) = 1-1 = 0. f(0) = 1-0 = 1.
In B f(1) = 1 - 1^2 = 0. f(0) = 1 - 0 = 1
In C f(1) = 1^2 - (1 - 1 )^2 = 1. f(0) = 0 - (1-0)^2 = 0 - 1 = -1
in D f(1) = 1(1-1)^2 = 0. f(0) = 0.(1-0)^2 = 0. ( Right answer )
And for option E you can take x = 2 because if you take x = 1 in denominator the denominator becomes zero, which makes the f(x) undefined.
f(2) = 2/(1 - 2) = -2. f(1-2) = f(-1) = -1/(1-(-1)) = -1/2.

D is the right answer.

Please give a kudo if you like my explanation.


This explanation is much more clear than the other one; now I have understood the question!!! :D

KUDOS
Current Student
avatar
B
Joined: 31 Jan 2016
Posts: 22
Schools: Rotman '19 (A)
Re: For which of the following functions f is f(x) = f(1-x) for all x? [#permalink]

Show Tags

New post 11 Apr 2016, 17:36
I honestly don't get this one. Please elaborate, stared at it for 2 and half hours. lol
Current Student
avatar
S
Joined: 20 Mar 2014
Posts: 2652
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: For which of the following functions f is f(x) = f(1-x) for all x? [#permalink]

Show Tags

New post 11 Apr 2016, 18:30
g3lo18 wrote:
I honestly don't get this one. Please elaborate, stared at it for 2 and half hours. lol


Have you gone through @Bunuel's solution at for-which-of-the-following-functions-f-is-f-x-f-1-x-for-85751.html#p644387 ? It is a well detailed and comprehensive solution.

As for the starting point, f(x) stands for a way to mention a relation in 'x'.

When I say, y=f(x), then there is a relation between y and x (it could be a linear relation in x or quadratic relation in x or cubic relation in x etc). In standard terms, we say that y is a function of x.

Now, in a similar fashion, if I mention y=f(1-x) ---> means that y is a function of (1-x).

The question is asking for the given 5 options of f(x), which of them will follow the relation f(x)=f(1-x) ---> simply check all the given options by substituting 1-x for x.

Example, option (a): f(x)=1-x ---> substitute 1-x for x ---> f(1-x)=1-(1-x) = 1-1+x = x \(\neq\) f(x). Keep working like this for other options and stop when you find the one that works.

Alternately, you can plug in x=0 and see which of the options gives you f(x)=f(1-x) ---> f(0) = f(1-0)=f(1).

Hope this helps.
Expert Post
SVP
SVP
avatar
B
Joined: 06 Nov 2014
Posts: 1891
Re: For which of the following functions f is f(x) = f(1-x) for all x? [#permalink]

Show Tags

New post 12 Jun 2016, 22:33
Given: f(x)= f(1-x)
This means if we replace x by 1 - x in the function, still the result should be same.

Checking each option:

A f(x)=1-x
f(1 - x) = 1 - (1-x) = x. Not equal to f(x)
INCORRECT

B f(x)=1-x^2
f(1-x) = 1- (1-x)^2 = 1 - (1 +x^2 - 2x). Not equal to f(x)
INCORRECT

C f(x)=x^2-(1-x)^2
f(1-x) = (1-x)^2 - (1 - 1 +x)^2 = (1-x)^2 -x^2. Not equal to f(x)
INCORRECT

D f(x)=x^2(1-x)^2
f(1-x) = (1-x)^2(1 - 1 + x)^2 = (1-x)^2*x^2.
This is equal to f(x)
CORRECT

E f(x)= x/(1-x)
f(1-x) = 1-x/1-x + x = (1-x)/x. Not equal to f(x)
INCORRECT

Correct Option: D
Expert Post
1 KUDOS received
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2447
Location: United States (CA)
Re: For which of the following functions f is f(x) = f(1-x) for all x? [#permalink]

Show Tags

New post 30 Mar 2017, 16:24
1
This post received
KUDOS
Expert's post
study wrote:
For which of the following functions f is f(x) = f(1-x) for all x?

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


Since we are not given any restrictions on the value of x, let’s let x = 1. Thus, we are determining for which of the following functions is f(1) = f(1-1), i.e., f(1) = f(0). Next, we can test each answer choice using our value x = 1.

A. f(x) = 1 - x

f(1) = 1 - 1 = 0

f(0) = 1 - 0 = 1

Since 0 does not equal 1, A is not correct.

B. f(x) = 1 - x^2

f(1) = 1 - 1^2 = 1 - 1 = 0

f(0) = 1 - 0^2 = 1 - 0 = 1

Since 0 does not equal 1, B is not correct.

C. f(x) = x^2 - (1 - x)^2

f(1) = 1^2 - (1 - 1)^2 = 1 - 0 = 1

f(0) = 0^2 - (1 - 0)^2 = 0 - 1 = -1

Since 1 does not equal -1, C is not correct.

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

f(1) = 1^2*(1 - 1)^2 = 1(0)= 0

f(0) = 0^2*(1 - 0)^2 = 0(2) = 0

Since 0 equals 0, D is correct.

Alternate Solution:

Let’s test each answer choice using x and 1 - x.

A. f(x) = 1 - x

f(x) = 1 - x

f(1 - x) = 1 - (1 - x) = x

Since 1 - x does not equal x, A is not correct.

B. f(x) = 1 - x^2

f(x) = 1 - x^2

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

Since 1 - x^2 does not equal 2x - x^2, B is not correct.

C. f(x) = x^2 - (1 - x)^2

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

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

Since 2x - 1 does not equal 1 - 2x, C is not correct.

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

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

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

Since x^2*(1 - x)^2 equals (1 - x)^2*x^2, D is correct.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Manager
Manager
avatar
B
Joined: 31 Dec 2016
Posts: 89
Re: For which of the following functions f is f(x) = f(1-x) for all x? [#permalink]

Show Tags

New post 18 Jul 2017, 17:37
Most people seem to suck at explaining these function related questions. Here is a good video explaining some function skills that helps on other questions. https://www.youtube.com/watch?v=T6-Zdr5w_bE

The key to these questions is understanding that f(x) is the function. Meaning that f(3) would mean everytime you see an x you sub in a 3. Or in this case we sub in an X-3. So for instance the first question is F(x) = 1-x............. Imagine the X is a blank or a blank parentheses waiting to be filled in by a number. so F(3) = 1-3 or F(x) = 1 - X or F (blank)= 1-(blank) or F(1-x) = 1-(1-x)
Attachments

Function question 6.png
Function question 6.png [ 417.34 KiB | Viewed 1203 times ]

Intern
Intern
avatar
B
Joined: 10 Dec 2017
Posts: 1
Re: For which of the following functions f is f(x) = f(1-x) for all x? [#permalink]

Show Tags

New post 23 Mar 2018, 09:21
Wow, Bunuel. Thank you for that explanation. After so much studying I have never seen such a simple explanation. Definitely one of those eye-opening moments. Plugging in x and x-1 to the expression must yield the same result.
Re: For which of the following functions f is f(x) = f(1-x) for all x?   [#permalink] 23 Mar 2018, 09:21

Go to page   Previous    1   2   [ 33 posts ] 

Display posts from previous: Sort by

For which of the following functions f is f(x) = f(1-x) for all x?

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.