Last visit was: 21 Apr 2026, 14:14 It is currently 21 Apr 2026, 14:14
Home
Messages
Tests
Schools
Events
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
User avatar
ast
User avatar
Joined: 27 Sep 2008
Last visit: 05 Oct 2008
Posts: 10
Own Kudos:
53
 [1]
Posts: 10
Kudos: 53
 [1]
Function f(x) satisfies f(x) = 03 Oct 2008, 23:11
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Function \(f(x)\) satisfies \(f(x) = f(x^2)\) for all \(x\) . Which of the following must be true?

* \(f(4) = f(2)f(2)\)
* \(f(16) - f(-2) = 0\)
* \(f(-2) + f(4) = 0\)
* \(f(3) = 3f(3)\)
* \(f(0) = 0\)



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
WinIT
User avatar
Joined: 10 Jul 2006
Last visit: 02 Nov 2008
Posts: 40
Own Kudos:
52
Posts: 40
Kudos: 52
Function f(x) satisfies f(x) = 04 Oct 2008, 05:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
* F(16)-f(-2)=0
On the above leads to f(16)-f(16).
User avatar
Greenberg
User avatar
Joined: 27 Sep 2008
Last visit: 10 Jul 2009
Posts: 32
Own Kudos:
42
Posts: 32
Kudos: 42
Function f(x) satisfies f(x) = 04 Oct 2008, 05:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Agree with (B)

f(x) = f(x^2)

f(-2) = f(4) = f(16)

:)
User avatar
ast
User avatar
Joined: 27 Sep 2008
Last visit: 05 Oct 2008
Posts: 10
Own Kudos:
53
 [1]
Posts: 10
Kudos: 53
 [1]
Function f(x) satisfies f(x) = 04 Oct 2008, 06:51
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can someone explain what each answer choice leads to?

And the logic behind solving the question...
User avatar
domleon
User avatar
Joined: 14 Jun 2007
Last visit: 22 May 2009
Posts: 77
Own Kudos:
88
Location: Vienna, Austria
Posts: 77
Kudos: 88
Function f(x) satisfies f(x) = 07 Oct 2008, 05:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
i think this is a cryptic one - can someone pls. each individual answer choice analyse (i know it´s bit of work, but it would really help those who are not 100% understaning the concept of functions).

many thanks in advance
dom
User avatar
Greenberg
User avatar
Joined: 27 Sep 2008
Last visit: 10 Jul 2009
Posts: 32
Own Kudos:
42
Posts: 32
Kudos: 42
Function f(x) satisfies f(x) = 07 Oct 2008, 13:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
domleon
i think this is a cryptic one - can someone pls. each individual answer choice analyse (i know it´s bit of work, but it would really help those who are not 100% understaning the concept of functions).

many thanks in advance
dom
Show more

Don't be fooled by big words like functions ect. there is nothing really to know.

In every function f(x) = 2x when you enter some value (lets assume x=2) you get a value (in this case 4) so if you just ignore the notation f(x) you can just write:

2x = ? for x=2

but a nice thing about functions is that you can take the outcome and reinstall it in the original function to get another (third) value.

f(x)=2x

f(x)=2(2x) = 4x

and so on ...

In this question you are not asked about values at all, you are being asked about functions and functions of functions so:

f(x) = f(x^2)

f(2) = f(2^2)

f(3) = f(3^3)

and so on...

we can't tell the value of f(2) = ?? only that it's equal to some f(4)

back to the question asked:

f(x) = f(x^2) is given

first line:

f(-2) = f(4) according to the given f(x) = f(x^2)

f(4) = f(16) according to the given f(x) = f(x^2)

f(4) = f(2)*f(2) ??

we have seen that f(4) = f(16) & f(2) = f(4) but we cannot say that f(4) = f(2)*f(2)

this may be true but we cannot say that from the given f(x) = f(x^2)

second line:

f(16)-f(-2) = 0

we can say that f(16) = f(-2) from the given data since:

f(-2) = f(4)

f(4) = f(16)

so we can say this is true !

third line:

f(-2)+f(4) = 0

we can't say if this is true since we don't know what is the value of f(-2) but we can tell that f(-2) = f(4) useless here !

forth line:

f(3) = 3f(3)

since f(3) = f(9)

I dont see how we can say this is true without knowing what f(3) = ??

fifth line:

f(0) = 0

we only know that f(0) = f(0) but we know nothing about 0


hopes this will help

:)
User avatar
domleon
User avatar
Joined: 14 Jun 2007
Last visit: 22 May 2009
Posts: 77
Own Kudos:
88
Location: Vienna, Austria
Posts: 77
Kudos: 88
Function f(x) satisfies f(x) = 09 Oct 2008, 01:22
Kudos
Add Kudos
Bookmarks
Bookmark this Post
greenberg -many thanks for the good explaination!



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!