Last visit was: 07 Jun 2026, 12:52 It is currently 07 Jun 2026, 12:52
Home
Messages
MBA Fair
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
Back to Forum
Create Topic
User avatar
Bismuth83
User avatar
DI Forum Moderator
Joined: 15 Sep 2024
Last visit: 01 Aug 2025
Posts: 712
Own Kudos:
3,318
 [8]
Given Kudos: 441
Expert
Expert reply
Posts: 712
Kudos: 3,318
 [8]
For all real values of [m]x[/m], the function [m]f(x)[/m] has the form 26 Mar 2025, 21:23
1
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide Answer
Hide
Show
History
v: 0 w: \(\frac{-1}{4}\)
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

86% (01:28) correct 14% (02:00) wrong based on 339 sessions

History

Date
Time
Result
Not Attempted Yet
For all real values of \(x\), the function \(f(x)\) has the form: \(f(x)=(x^2−4)^{−1}\). Select one value for \(v\) and one value for \(w\) that fulfills the condition that \(f(v) = w.\)
v w
\(\frac{-1}{4}\)
0
\(\frac{1}{4}\)
\(\frac{1}{3}\)
3
4
Submit Answer
Start the Timer above, select the radio buttons, and click "Submit" to add this question to your Error log.
ShowHide Answer
Official Answer
v: 0 w: \(\frac{-1}{4}\)
User avatar
HarshavardhanR
User avatar
Joined: 16 Mar 2023
Last visit: 07 Jun 2026
Posts: 527
Own Kudos:
601
 [3]
Given Kudos: 73
Status:Independent GMAT Tutor
Affiliations: Ex - Director, Subject Matter Expertise at e-GMAT
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 527
Kudos: 601
 [3]
For all real values of [m]x[/m], the function [m]f(x)[/m] has the form 26 Mar 2025, 22:44
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Attachment:
GMAT-Club-Forum-sz5y943x.png
GMAT-Club-Forum-sz5y943x.png [ 108.64 KiB | Viewed 2113 times ]

Harsha
User avatar
GmatTest2026
User avatar
Joined: 30 Jul 2019
Last visit: 07 Jun 2026
Posts: 1,636
Own Kudos:
789
Given Kudos: 3,867
Location: India
Concentration: General Management, Economics
Schools: Duke '27
GPA: 3
WE:Human Resources (Real Estate)
Schools: Duke '27
Posts: 1,636
Kudos: 789
For all real values of [m]x[/m], the function [m]f(x)[/m] has the form 26 Mar 2025, 23:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bismuth83
For all real values of \(x\), the function \(f(x)\) has the form: \(f(x)=(x^2−4)^{−1}\). Select one value for \(v\) and one value for \(w\) that fulfills the condition that \(f(v) = w.\)
Show more
Solution

\(f(x)=(x^2−4)^{−1}\) can be expressed as \(\frac{1}{(x+2)(x-2)}\). This tells us the value for x can be -2 or 2, and when assigning these values back to the equation, we will get two results,\(\frac{1}{(2+2)(2-2)}\)= 0 and \(\frac{1}{(-2+2)(-2-2)}\)=0. So, the value for v = 0 and from this if put 0 back to the given equation then we will get\( \frac{1}{(0^2-4)}\)=\( \frac{-1}{4}\) the value for w.


Bismuth83, is this approach correct?
User avatar
agrotechpepper
User avatar
Joined: 26 Apr 2024
Last visit: 12 Jan 2026
Posts: 29
Own Kudos:
8
 [1]
Given Kudos: 389
Posts: 29
Kudos: 8
 [1]
For all real values of [m]x[/m], the function [m]f(x)[/m] has the form 02 Jul 2025, 04:35
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
No, you cant equate denominator to 0, it would make the function undefined. In the given function, x can take any values other than 2 and -2.
poojaarora1818
Bismuth83
For all real values of \(x\), the function \(f(x)\) has the form: \(f(x)=(x^2−4)^{−1}\). Select one value for \(v\) and one value for \(w\) that fulfills the condition that \(f(v) = w.\)
Solution

\(f(x)=(x^2−4)^{−1}\) can be expressed as \(\frac{1}{(x+2)(x-2)}\). This tells us the value for x can be -2 or 2, and when assigning these values back to the equation, we will get two results,\(\frac{1}{(2+2)(2-2)}\)= 0 and \(\frac{1}{(-2+2)(-2-2)}\)=0. So, the value for v = 0 and from this if put 0 back to the given equation then we will get\( \frac{1}{(0^2-4)}\)=\( \frac{-1}{4}\) the value for w.


Bismuth83, is this approach correct?
Show more
User avatar
GmatTest2026
User avatar
Joined: 30 Jul 2019
Last visit: 07 Jun 2026
Posts: 1,636
Own Kudos:
789
Given Kudos: 3,867
Location: India
Concentration: General Management, Economics
Schools: Duke '27
GPA: 3
WE:Human Resources (Real Estate)
Schools: Duke '27
Posts: 1,636
Kudos: 789
For all real values of [m]x[/m], the function [m]f(x)[/m] has the form 03 Jul 2025, 12:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thank you so much for your response. I appreciate it!
agrotechpepper
No, you cant equate denominator to 0, it would make the function undefined. In the given function, x can take any values other than 2 and -2.
poojaarora1818
Bismuth83
For all real values of \(x\), the function \(f(x)\) has the form: \(f(x)=(x^2−4)^{−1}\). Select one value for \(v\) and one value for \(w\) that fulfills the condition that \(f(v) = w.\)
Solution

\(f(x)=(x^2−4)^{−1}\) can be expressed as \(\frac{1}{(x+2)(x-2)}\). This tells us the value for x can be -2 or 2, and when assigning these values back to the equation, we will get two results,\(\frac{1}{(2+2)(2-2)}\)= 0 and \(\frac{1}{(-2+2)(-2-2)}\)=0. So, the value for v = 0 and from this if put 0 back to the given equation then we will get\( \frac{1}{(0^2-4)}\)=\( \frac{-1}{4}\) the value for w.


Bismuth83, is this approach correct?
Show more
User avatar
svsivakrishna
User avatar
Joined: 12 May 2024
Last visit: 31 Jan 2026
Posts: 78
Own Kudos:
34
Given Kudos: 180
Posts: 78
Kudos: 34
For all real values of [m]x[/m], the function [m]f(x)[/m] has the form 06 Jul 2025, 20:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given f(x)=(x^2−4) ^ (−1)
To find: v and w such that
they fulfill the condition f(v)=w.

Therefore w=1/(v^2-4)

Considering from the answer choices, select v=0, then w= -1/4, both of which satisfy the given options.
Moderators:
Bunuel
Math Expert
111124 posts
Gmat860sanskar
343 posts