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

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATBootcamp Starts Sep 28
Chris Peckover, Target Test Prep GMAT expert
LIVE ONLINE BOOTCAMP

Live Online Bootcamp Class with Top GMAT Expert Chris Peckover

15 live classes from Sep 28, 2026

Schedule
Mon to Fri · 7:00 to 10:00 PM ET
Included
Live classes + 6 months of TTP OnDemand
  • Boost your GMAT score in less than one month in a live online class
  • 6 months access to TTP OnDemand video courses included
View bootcamp & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

Help on PS problem- GMATprep

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 418
Joined: Mon Feb 26, 2007 6:41 pm
Thanked: 24 times
by Prasanna » Sun Apr 29, 2007 4:22 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)

The answer is d. Need help in solving this.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 986
Joined: Wed Dec 20, 2006 11:07 amFollowed by: 1 member
Location: India
Thanked: 51 times

Re: Help on PS problem- GMATprep

by gabriel » Sun Apr 29, 2007 5:11 am
Prasanna 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)

The answer is d. Need help in solving this.
Hi prassana .... when we say f(x)=f(1-x) ... it means that the eqn that represents f(x) should not change when x is replaced with (1-x) in that eqn .. and if u see it is only true for d ... for d it is given f(x) = x^2(1-x)^2 .. to find f(1-x) replace x with 1-x ... so we have f(1-x)= (1-x)^2(1-(1-x))^2 = (1-x)^2x^2 ... which is the same as f(x).. so D ....
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 418
Joined: Mon Feb 26, 2007 6:41 pm
Thanked: 24 times

by Prasanna » Sun Apr 29, 2007 10:31 am
Gabriel

Thanks for the answer.

I had made a mistake in my calculations :oops:

Prasanna
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 559
Joined: Tue Mar 27, 2007 1:29 amFollowed by: 2 members
Thanked: 5 times

by Cybermusings » Mon Apr 30, 2007 1:14 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)

a) f(x) = 1-x
f(1-x) = 1-1+x = x
Hence f(x) is not equal to f(1-x)

b) f(x) = [1-x^2]
f(1-x) = [1-(1-x)^2]
= [1-(1+x^2-2)]
=[2-x^2]
Hence f(x) is not equal to f(1-x)

c) f(x) = x^2-(1-x)^2
=x^2 - [ 1+x^2-2x]
=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 + x^2 - 2x - x^2
= 1-2x

d)f(x)=x^2(1-x)^2
f(x) = x^2(1+x^2-2x)
=x^2+x^4-2x^3

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

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

Hence D
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8199
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

by Scott@TargetTestPrep » Mon May 20, 2019 6:16 pm
Prasanna 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
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Tue May 21, 2019 6:16 am
Prasanna 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)

The answer is d. Need help in solving this.
Let's test the values using x = 0

So, we can reword the question as, For which of the following functions is f(0)=f(1-0)
In other words, we're looking for a function such that f(0) = f(1)

A) f(x)=1-x
f(0)=1-0 = 1
f(1)=1-1 = 0
Since f(0) doesn't equal f(1), eliminate A

B) f(x) = 1 - x²
f(0) = 1 - 0² = 1
f(1) = 1 - 1² = 0
Since f(0) doesn't equal f(1), eliminate B

C) f(x) = x² - (1-x)²
f(0) = 0² - (1-0)² = -1
f(1) = 1² - (1-1)² = 1
Since f(0) doesn't equal f(1), eliminate C

D) f(x) = x²(1-x)²
f(0) = 0^2(1-0)^2 = 0
f(1) = 1^2(1-1)^2 = 0
Since f(0) equals f(1), keep D for now

E) f(x) = x/(1-x)
f(0) = 0/(1-0) = 0
f(1) = 1/(1-1) = undefined
Since f(0) doesn't equal f(1), eliminate E

Since only D satisfies the condition that f(x)=f(1-x) when x=0, the correct answer is D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1