NEW HERE? LEARN MORE
closeclose
Last visit was: 02 May 2024, 02:21 It is currently 02 May 2024, 02:21
Decision Tracker
My Rewards
New posts
New comers' posts

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

The function f is defined by f(x) = ax^4

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
carcass
Board of Directors
Joined: 01 Sep 2010
Posts: 4393
Own Kudos [?]: 32930 [4]
Given Kudos: 4460
Send PM
The function f is defined by f(x) = ax^4 [#permalink] New post   28 Aug 2023, 11:20
1
Kudos
3
Bookmarks
Top Contributor
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

74% (01:15) correct 26% (02:18) wrong based on 74 sessions
Hide Show timer Statistics
The function f is defined by \(f(x) = ax^4 – 4x^2 + ax – 3\) for all numbers x. What will \(f(b) – f(–b)\) equal?

A. 0
B. \(2ab\)
C. \(–8b^2 – 6\)
D. \(2ab^4 –8b^2 – 6\)
E. \(2ab^4 –8b^2 + 2ab – 6\)


Post A Detailed Correct Solution For The Above Questions And Get Kudos.
ShowHide Answer
Official Answer
B
User avatar
P
divyadna
Senior Manager
Senior Manager
Joined: 21 Dec 2021
Posts: 334
Own Kudos [?]: 242 [2]
Given Kudos: 242
Send PM
Re: The function f is defined by f(x) = ax^4 [#permalink] New post   28 Aug 2023, 11:46
2
Kudos
f(b)= ab^4-4b^2+ab-3
f(-b)= ab^4-4b^2-ab-3
f(b)-f(-b)= ab^4-ab^4-4b^2+4b^2+ab+ab-3+3
= 2ab
Option B is the answer

Posted from my mobile device
User avatar
L
gmatophobia
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3107
Own Kudos [?]: 4201 [1]
Given Kudos: 1851
Location: India
Concentration: Strategy, Leadership
Send PM
CAT Tests Forum Quiz Mode
Re: The function f is defined by f(x) = ax^4 [#permalink] New post   28 Aug 2023, 12:35
1
Kudos
carcass wrote:
The function f is defined by \(f(x) = ax^4 – 4x^2 + ax – 3\) for all numbers x. What will \(f(b) – f(–b)\) equal?

A. 0
B. \(2ab\)
C. \(–8b^2 – 6\)
D. \(2ab^4 –8b^2 – 6\)
E. \(2ab^4 –8b^2 + 2ab – 6\)


Assume :

  • b = 1
  • -b = -1

f(b) = a - 4 + a - 3 = 2a - 7

f(-b) = a - 4 - a - 3 = - 7

f(b) - f(-b) = 2a - 7 + 7 = 2a

Answer choice elimination

A. 0 → Eliminate

B. \(2ab\) → 2a

Matches with expected answer → Keep

C. \(–8b^2 – 6\) → Eliminate as the value is independent of a

D. \(2ab^4 –8b^2 – 6\)→ \(2a - 8 - 6 = 2a - 14\)

Eliminate

E. \(2ab^4 –8b^2 + 2ab – 6\) → \(2a - 8 + 2a - 6 = 4a - 14\)

Eliminate

Option B
User avatar
D
BrushMyQuant
Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1778
Own Kudos [?]: 2097 [0]
Given Kudos: 100
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Send PM
The function f is defined by f(x) = ax^4 [#permalink] New post   18 Nov 2023, 02:34
Expert Reply
Top Contributor
\(f(x) = ax^4 – 4x^2 + ax – 3\) and we need to find the value of \(f(b) – f(–b)\)

Now, f(b) and f(-b) will have same terms but
    - Terms with even power of b will have same sign
    - Terms with odd power of b will have different sign
    - Constant terms with no power of b will have same sign

So, if we are finding the value of f(b) - f(-b) then the terms with same sign will cancel out and we will be left with terms with different signs only

=> f(b) - f(-b) = ab - (a*-b) = 2ab

Detailed step by step solution

f(b) - f(-b) = \(ab^4 – 4b^2 + ab – 3 - (a(-b)^4 – 4(-b)^2 + a(-b) – 3\) = \(ab^4 - ab^4 – 4b^2 + 4b^2 + ab + ab – 3 + 3\) = 2ab

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

GMAT Club Bot
gmatclubot
The function f is defined by f(x) = ax^4 [#permalink]
18 Nov 2023, 02:34
Moderators:
Bunuel
Math Expert
93001 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions