Last visit was: 11 Jul 2025, 05:25 It is currently 11 Jul 2025, 05:25
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.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Jul 2025
Posts: 102,634
Own Kudos:
Given Kudos: 98,170
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,634
Kudos: 740,343
 [11]
1
Kudos
Add Kudos
10
Bookmarks
Bookmark this Post
User avatar
TestPrepUnlimited
Joined: 17 Sep 2014
Last visit: 30 Jun 2022
Posts: 1,226
Own Kudos:
Given Kudos: 6
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Expert
Expert reply
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Posts: 1,226
Kudos: 1,067
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
BrushMyQuant
Joined: 05 Apr 2011
Last visit: 10 Jul 2025
Posts: 2,243
Own Kudos:
2,458
 [1]
Given Kudos: 100
Status:Tutor - BrushMyQuant
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
Posts: 2,243
Kudos: 2,458
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
User avatar
Dyaneth
Joined: 13 Oct 2021
Last visit: 21 Dec 2024
Posts: 5
Own Kudos:
Given Kudos: 186
Posts: 5
Kudos: 18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
f(x+y)+f(x−y)= \( \frac{C^{x}*C^{y}+C^{-x}*C^{-y}}{2} +\frac{ C^{x}*C^{-y}+C^{-x}*C^{y}}{2}\)

f(x+y)+f(x−y)= \( \frac{C^{-x}*(C^{y}+C^{-y}) + C^{x}*(C^{y}+C^{-y})}{2}\)

f(x+y)+f(x−y)= \( \frac{(C^{y}+C^{-y})}{2} * \frac{(C^{x}+C^{-x})}{2}\) * 2

f(x+y)+f(x−y) = 2*f(y)*f(x)

Answer: D
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 11 Jul 2025
Posts: 5,690
Own Kudos:
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
GMAT 1: 690 Q50 V34
Posts: 5,690
Kudos: 5,205
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let a function be defined as \(f(x) = \frac{c^x + c^{-x}}{2}\), for \(c > 0\).

What is the value of \(f(x + y) + f(x - y) \)?

\(f(x) = \frac{c^x + c^{-x}}{2}\)

\(f(x+y) = \frac{c^{x+y} + c^{-x-y}}{2}\)
\(f(x-y) = \frac{c^{x-y} + c^{y-x}}{2}\)
\(f(x+y) + f(x-y) = \frac{c^{x+y} + c^{-x-y}}{2}+\frac{c^{x-y} + c^{y-x}}{2} = \frac{c^x(c^y+c^{-y})}{2} + \frac{c^{-x}(c^y + c^{-y})}{2} = 2(\frac{c^x + c^{-x}}{2})(\frac{c^y + c^{-y}}{2}) = 2f(x)f(y) \)

IMO D
Moderators:
Math Expert
102634 posts
PS Forum Moderator
686 posts