BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

function f(x)

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 273
Joined: Thu Sep 08, 2011 6:50 am
Thanked: 5 times
Followed by:3 members

function f(x)

by fangtray » Wed Apr 04, 2012 5:56 am
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)

i plugged in f[1-(1-x)] and got f(x). so i thought the answer was a. could someone show me how this works?
Top
Source: — Problem Solving |
User avatar
Community Manager
Posts: 1060
Joined: Fri May 13, 2011 6:46 am
Location: Utrecht, The Netherlands
Thanked: 318 times
Followed by:52 members

by neelgandham » Wed Apr 04, 2012 6:05 am
fangtray 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)
Easiest way to solve this PS is substitution

Let x = 1, then 1-x = 0, so f(1) = f(0)
a. f(x) = 1-x, f(1) = 0, f(0) = 1, f(x) is not equal to f(1-x), Incorrect
b. f(x) = 1-(x^2), f(1) = 0, f(0) = 1, f(x) is not equal to f(1-x), Incorrect
c. f(x) = (x^2)-(1-x)^2, f(1) = 1, f(0) = -1, f(x) is not equal to f(1-x), Incorrect
d. f(x) = (x^2)(1-x)^2, f(1) = 0, f(0) = 0, Correct!! Yippie! [spoiler]<-- answer[/spoiler]
e. f(x) = x/(1-x), f(1) = Not defined, f(0) = 0, Incorrect
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Wed Apr 04, 2012 6:11 am
I posted a solution here:

https://www.beatthegmat.com/gmatprep-ps- ... 91553.html
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Wed Apr 04, 2012 7:11 pm
fangtray 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)

i plugged in f[1-(1-x)] and got f(x). so i thought the answer was a. could someone show me how this works?

Let us look at each of the options:

(A) f(x) = 1-x
f(1-x) = 1 - (1-x) = x; FALSE

(B) f(x) = 1-x^2
f(1-x) = 1 - (1-x)^2 = 1 - (1 - 2x + x^2) = 2x - x^2; FALSE

(C) f(x) = x^2 - (1-x)^2
f(1-x) = (1-x)^2 - (1 - (1-x))^2 = 1 - 2x + x^2 - (x)^2 = 1 - 2x; FALSE

(D) f(x) = x^2 * (1-x)^2
f(1-x) = (1 - x)^2 * (1 - (1 - x))^2 = (1 - x)^2 * (x)^2; TRUE

(E) f(x) = x/(1-x)
so f(1-x) = (1-x)/(1-(1-x)) = (1-x)/x; FALSE

The correct answer is D.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
User avatar
Junior | Next Rank: 30 Posts
Posts: 15
Joined: Mon Mar 26, 2012 12:14 am
Thanked: 3 times

by gmatmath » Fri Apr 06, 2012 7:09 am
In this question, we will be deriving teh answer from the choices.
a) f(x) = 1-x
==> f(1-x) = 1-(1-x)= x
hence f(x) not= f(1-x)

b)f(x) = 1-x^2
f(1-x) = 1-(1-x)^2
= 1-(1+(x^2)-2x)
= (-x^2)+2x
here, f(x) not=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)
f(x) not = f(1-x), hence not the solution

d) f(x) = (x^2)(1-x)^2
f(1-x) = (1-x)^2.(1-(1-x))^2
= (1-x)^2.(x^2)
Here, plz observe that f(x) and f(1-x) are the same. Hence option D is the answer.
Top
Post new topic Post Reply
• Page 1 of 1