Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 06 May 2015, 14:59

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# For which of the following functions f is f(x) = f(1 - x)

Author Message
TAGS:
Director
Joined: 27 Dec 2004
Posts: 908
Followers: 1

Kudos [?]: 19 [0], given: 0

For which of the following functions f is f(x) = f(1 - x) [#permalink]  21 Aug 2005, 18:27
For which of the following functions f is f(x) = f(1 - x) for all x?

1. f(x) = 1-x

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

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

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

5. f(x) x / (1-x)
Senior Manager
Joined: 04 May 2005
Posts: 284
Location: CA, USA
Followers: 1

Kudos [?]: 22 [0], given: 0

Re: Function [#permalink]  22 Aug 2005, 06:11
Folaa3 wrote:
For which of the following functions f is f(x) = f(1 - x) for all x?

1. f(x) = 1-x

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

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

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

5. f(x) x / (1-x)

4. Only it has 'x' and '1-x' listed as symetrically
SVP
Joined: 03 Jan 2005
Posts: 2250
Followers: 13

Kudos [?]: 217 [0], given: 0

Re: Function [#permalink]  23 Aug 2005, 05:47
Yes, that is a very good way to view it. For people who want to make absolutely sure, or for more complicated problems, one would have to actually plug it in and try it out.

1. f(x) = 1-x
f(1-x)=1-(1-x)=x
No

2. f(x) = 1 - x^2
f(1-x)=1-(1-x)^2
No

3. f(x) = x^2 - (1 - x) ^2
f(1-x)=(1-x)^2-x^2=-f(x)
No

4. f(x) = x^2 ( 1 - x) ^2
f(1-x)=(1-x)^2x^2=f(x)
Yes

5. f(x) = x / (1-x)
f(1-x)=(1-x)/x
No
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

Senior Manager
Joined: 30 May 2005
Posts: 374
Followers: 1

Kudos [?]: 7 [0], given: 0

Just plug in the values! If the algebra looks bad, use some non-trivial numbers and see. For instance use x = 3, 1-x=-2
SVP
Joined: 03 Jan 2005
Posts: 2250
Followers: 13

Kudos [?]: 217 [0], given: 0

Or better yet use x=0 and 1-x=1. However to use number plugins you need to be very very careful. If it turns out that they produce different values then you are ok, as only one counter example would be sufficient to say No. If it turns out that they do produce the same value, however, you can't simply say yes, for there may be other numbers that would make the two functions produce different values.
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

VP
Joined: 18 Nov 2004
Posts: 1442
Followers: 2

Kudos [?]: 20 [0], given: 0

Re: Function [#permalink]  23 Aug 2005, 12:15
For these kind of questions, the fastest way is to substitute 1-x in place of x in the f(x) ...see below....OA shud be "4".Plugging shud be the last measure as it can lead to erroneous conclusions and it takes time.

Folaa3 wrote:
For which of the following functions f is f(x) = f(1 - x) for all x?

1. f(x) = 1-x ---> f(1-x) = 1-(1-x) = x <> 1-x ....out
2. f(x) = 1 - x^2 ----> f(1-x) = 1-(1-x)^2 = 2x - x^2 <> 1-x^2 ...out

3. f(x) = x^2 - (1 - x) ^2 ----> f(1-x) = (1-x)^2 - x^2 ....no always true
4. f(x) = x^2 ( 1 - x) ^2 ---> f(1-x) = (1-x)^2 x^2 = f(x).....right

5. f(x) = x / (1-x) ----> f(1-x) = (1-x)/x.....<> f(x) .....not true
Senior Manager
Joined: 29 Nov 2004
Posts: 486
Location: Chicago
Followers: 1

Kudos [?]: 9 [0], given: 0

4) SUbstituting (x-1) in place of x gives the same value....
_________________

Fear Mediocrity, Respect Ignorance

Similar topics Replies Last post
Similar
Topics:
For which of the following functions f is f(x) = f (1-x) 0 04 Aug 2013, 07:25
2 For which of the following functions f is f(x) = f(1-x) for 15 28 Jun 2011, 07:12
For which of the following functions f is f(x) = f(1-x) for 4 18 Aug 2008, 12:58
For which of the following function f is f(x) = f(1-x) for 3 23 Dec 2007, 21:17
For which of the following functions f is f(x)= f(1-x) for 1 17 Oct 2007, 18:20
Display posts from previous: Sort by