Aug 19 08:00 AM PDT  09:00 AM PDT Join a 4day FREE online boot camp to kick off your GMAT preparation and get you into your dream bschool in R1.**Limited for the first 99 registrants. Register today! Aug 20 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Aug 20 09:00 PM PDT  10:00 PM PDT Take 20% off the plan of your choice, now through midnight on Tuesday, 8/20 Aug 22 09:00 PM PDT  10:00 PM PDT What you'll gain: Strategies and techniques for approaching featured GMAT topics, and much more. Thursday, August 22nd at 9 PM EDT Aug 24 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 57026

Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 08:00
Question Stats:
70% (01:32) correct 30% (01:39) wrong based on 284 sessions
HideShow timer Statistics
Which of the following function follows the rule: \(f(a + b) = f(a)*f(b)\)? A. \(f(x)= x^2 +1\) B. \(f(x)= \frac{5^{2x}}{3}\) C. \(f(x)= 3x+2\) D. \(f(x)= \sqrt{2x}\) E. \(f(x)= 24^x\)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Manager
Joined: 31 May 2018
Posts: 183
Location: United States
Concentration: Finance, Marketing

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 08:08
f(a+b)=f(a)∗f(b)
E ) f(x)=\(24^x\)
f(a+b) = 24^(a+b)
f(a)∗f(b)= \(24^a\)*\(24^b\)=24^(a+b)....(properties of exponent)
hence in option E f(a+b)=f(a)∗f(b) answer




VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1031
WE: Supply Chain Management (Energy and Utilities)

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 08:12
Clearly the answer is (E). Property of exponent used: (a^m)*(a^n)=a^(m+n) f(a+b)=24^(a+b)=(24^a)*(24^b)=f(a)*f(b)
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Senior Manager
Joined: 12 Dec 2015
Posts: 427

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 08:14
Which of the following function follows the rule: f(a+b)=f(a)∗f(b)?
A. f(x)=x2+1
B. f(x)=5^(2x)/3
C. f(x)=3x+2
D. f(x)=√(2x)
E. f(x)=24^x > correct: f(a+b) = 24^(a+b) = 24^a * 24^b = f(a)*f(b)



Manager
Joined: 29 Nov 2018
Posts: 144
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.99
WE: Engineering (Computer Hardware)

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 08:17
f(x)=x^2+1  not correct f(a+b) = (a+b)^2 + 1 which is not equal to (a^2+1)(b^2+1)
B. f(x)=(5^(2x))/3  not correct f(a+b) = (5^(2a+2b))/3 not equal to (5^(2a))/3 * (5^(2b))/3
C. f(x)=3x+2  not correct f(a+b) = 3(a+b) + 2 not equal to (3a+2)*(3b+2)
D. f(x)=sqrt(2x) not correct sqrt (a+b) is not equal to sqrt(a)*sqrt(b)
E. f(x)=24^x  correct 24^(a+b) = 24^a * 24^b



GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4464
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 08:22
IMO E; for the given function of the set ; f(a+b)=f(a)∗f(b)f(a+b)=f(a)∗f(b) substitute value of function of x for option E ; f(x)=24x we get 24^(a+b) = 24^a*24^b Which of the following function follows the rule: f(a+b)=f(a)∗f(b)f(a+b)=f(a)∗f(b)? A. f(x)=x2+1f(x)=x2+1 B. f(x)=52x3f(x)=52x3 C. f(x)=3x+2f(x)=3x+2 D. f(x)=2x‾‾√f(x)=2x E. f(x)=24x
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.



Manager
Joined: 30 May 2018
Posts: 146
Location: Canada
GPA: 3.8

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 08:23
E.
f(a+b) = 24^(a+b) f(a)*f(b) = 24^a*24^b = 24^(a+b)



Manager
Joined: 25 Jul 2018
Posts: 187

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 08:24
f(a+b)=f(a)∗f(b)? E. f(x)=24^x f(a+b)=24^(a+b)
f(a)=24^a f(b)=24^b > 24^(a+b)=24^a*24^b=24^(a+b) Answer choice is E.



Manager
Joined: 10 Aug 2018
Posts: 212
Location: India
Concentration: Strategy, Operations
WE: Operations (Energy and Utilities)

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 08:26
E is the correct answer as powers of 24 will add. Posted from my mobile device
_________________
On the way to conquer the GMAT and I will not leave it until I win. WHATEVER IT TAKES. Target 720+ " I CAN AND I WILL"Your suggestions will be appreciated: https://gmatclub.com/forum/youroneadvicecouldhelpmepoorgmatscores299072.html1) Gmat prep: 620 Q48, V27 2) Gmat prep: 610 Q47, V28 3) Gmat prep: 620 Q47, V28 4) Gmat prep: 660 Q47, V34 5) Gmat prep: 560 Q37, V29 6) Gmat prep: 540 Q39, V26 7) Veritas Cat: 620 Q46, V30 8) Veritas Cat: 630 Q45, V32



Manager
Joined: 27 May 2010
Posts: 200

Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
Updated on: 09 Jul 2019, 01:54
f(a+b)=f(a)∗f(b) Lets assume values for a and b. Let a = 2 and b =3 A. f(x)=x^2+1 f(2) = 5, f(3) = 10 f(2)*f(3) = 50 f(2+3) = f(5) = 26 f(2)*f(3) not equals f(2+3) Therefore not right B. f(x)=5^2x/3 f(2) = 5^4/3, f(3) = 5^6/3 f(2)*f(3) = (5^4 * 5^6)/(3*3) = 5^10/9 f(5) = 5^10/3 f(2)*f(3) not equals f(2+3) Therefore not right C. f(x)=3x+2 f(2) = 8, f(3) = 11 f(2)*f(3) = 88 f(5) = 17 f(2)*f(3) not equals f(2+3) Therefore not right D. f(x)=√2x f(2) = \(\sqrt{4}, f(3) = \sqrt{6}\) f(2)*f(3) = \(\sqrt{24}\) f(5) = \(\sqrt{10}\) f(2)*f(3) not equals f(2+3) Therefore not right E. f(x)=24^x f(2) = 24^2, f(3) = 24^3 f(2)*f(3)= 24^5 f(5) = 24^5 f(2)*f(3) equals f(2+3) Therefore E is the answer. Posted from my mobile device
_________________
Please give Kudos if you like the post
Originally posted by prashanths on 08 Jul 2019, 08:31.
Last edited by prashanths on 09 Jul 2019, 01:54, edited 2 times in total.



Intern
Joined: 26 May 2017
Posts: 26
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.34
WE: General Management (Energy and Utilities)

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 08:31
Simple substitution gives: A. f(a+b) = (a+b)^2+1 f(a)*f(b) = (a^2+1)*(b^2+1) Since both are not equal, A is Wrong.
B. f(a+b) = (5^2(a+b))/3 f(a)*f(b) = (5^2(a+b))/3 Since both are equal, B is Correct.
C. f(a+b) = 3(a+b) +2 f(a)*f(b) =(3a+2)*(3b+2) Since both are not equal, C is Wrong.
D. f(a+b) = sqrt(2a+2b) f(a)*f(b) = \sqrt{2a} +\sqrt{2b} Since both are not equal, D is Wrong.
E. f(a+b) = 24^(a+b) f(a)*f(b) = 24^(a+b) Since both are equal, E is Correct.



Senior Manager
Joined: 24 Nov 2016
Posts: 308
Location: United States

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 08:32
Quote: Which of the following function follows the rule: f(a+b)=f(a)∗f(b)f(a+b)=f(a)∗f(b)?
A. f(x)=x2+1
B. f(x)=52x3
C. f(x)=3x+2
D. f(x)=2x‾‾√
E. f(x)=24x (a) is (a+b)ˆ2+1=(aˆ2+1)(bˆ2+1)? no. (b) is (5)ˆ2(a+b)/3=(5)ˆ2(a+b)/9? no. (c) is 3(a+b)+2=(3(a)+2)(3(b)+2)? no. (d) is √2(a+b)=2√ab? no. Answer (E): 24ˆ(a+b)=24^a*24^b=24^(a+b)



Manager
Joined: 08 Apr 2019
Posts: 149
Location: India
GPA: 4

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 08:36
Quickest way  put in values of a+b and a & b in the given functions
f(x)=x^2+1; f(a+b)=(a+b)^2+1 and f(a)=a^2+1 * f(b)=b^2+1 CLEARLY NO
f(x)=5^2x/3, now solving this will give you a clear hint that this is not the answer since the denominator on the right and side will be 3*3, which was a pretty clear indication for me to jump straight to option (E)
f(x)=24^x; f(a+b)=24^(a+b) and f(a)=24^a * f(b)=24^b, now since we know that when the base is same the powers add, this makes it the correct answer choice, and hence, (E) is our correct answer choice



Director
Joined: 28 Jul 2016
Posts: 534
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)

Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 08:37
Which of the following function follows the rule: f(a+b)=f(a)∗f(b)?
A. f(x)=x2+1
B. f(x)=5^2x/3
C. f(x)=3x+2
D. f(x)=2x
E. f(x)=24^x
evaluating expressions should be of the form f(a+b) =f(a)*f(b)
Most are multiliplaction generally powers have a rule of x^a *x^b = x^(a+b) i saw E as first such option and put in the value \(24^a*24^y = 24^(a+b)\) Which fulfils the given expression
Hence answer is E



Director
Joined: 19 Oct 2018
Posts: 769
Location: India

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 08:38
A. \((a+b)^2+1=a^2+b^2+2ab+\)1 which is not necessarily equals to \((a^2+1)*(b^2+1)\) B. \(\frac{5^{2a+2b}}{3}\)= \(\frac{5^{2a}}{3}\)*\(5^{2b}\), not equal to \(\frac{5^{2a}}{3}\)* \(\frac{5^{2b}}{3}\)
C. 3(a+b)+2=3a+3b+2 is not equal to (3a+2)*(3b+2) D. \(\sqrt{2(a+b)}\) is not equal to \(\sqrt{2a}*\sqrt{2b}\) E. \(24^{a+b}=24^a*24^b\)
IMO E



Manager
Joined: 12 Apr 2017
Posts: 132
Location: United States
Concentration: Finance, Operations
GPA: 3.1

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 08:41
I chose D,
I believe the question is asking,
For what two numbers inserted into the function will result in the same answer when the two same numbers are multiplied together.
Plugging in F(2 + 2) = F(2) * (2), the only result of the answer choices to match that was D. 2 = 2 when plugged in.



Intern
Joined: 15 Jun 2019
Posts: 32
Location: Kazakhstan
GPA: 3.93

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 08:44
A. f(x)=x^2+1 f(a+b)=(a+b)^2+1=a^2+b^2+2ab+1 f(a)*f(b) = (a^2+1)*(b^2+1)=a^2*b^2+a^2+b^2+1 f(a+b) doesn't equal f(a)*f(b)
B. f(x)=5^(2x)/3 f(a+b)=5^2(a+b)/3 f(a)f(b) = 5^(2a)/3*5^(2b)/3=5^(2a+2b)/9 f(a+b) doesn't equal f(a)*f(b)
C. f(x)=3x+2 f(a+b)=3(a+b)+2 f(a)f(b) = (3a+2)(3b+2) f(a+b) doesn't equal f(a)*f(b)
D. f(x)=(2x)^(1/2) f(a+b)=(2(a+b))^(1/2) f(a)f(b) = (2a)^1/2 * (2b)^1/2 = 2(ab)^1/2 f(a+b) doesn't equal f(a)*f(b)
E. f(x)=24^x f(a+b)=24^(a+b)=24^a*24^b f(a)f(b) = 24^a*24^b
Answer: E



Manager
Joined: 18 Sep 2018
Posts: 100

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 08:46
IMO E
A. f(x)=x^2+1 => f(a+b) = a^2+b^2+2ab+1; f(a)*f(b) = (a^2+1)(b^2+1) = a^2*b^2+a^2+b^2+1
B. f(x)=(5^(2x))/3 = (25^x)/3 => f(a+b) = (25^(a+b))/3 = (25^a*25^b)/3; f(a)*f(b) = ((25^a)/3)*((25^b)/3) = (25^a*25^b)/9
C. f(x)=3x+2 => f(a+b) = 3a+3b+2; f(a)*f(b) = (3a+2)(3b+2) = 9ab+3a+3b+4
D. f(x)=√(2x) => f(a+b) = √(2a+2b); f(a)*f(b) = √(2a)*√(2b) = 2√(ab)
E. f(x)=24^x => f(a+b) = 24^(a+b) = (24^a)*(24^b) = f(a)*f(b)



Manager
Joined: 24 Jun 2019
Posts: 108

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 08:47
Which of the following function follows the rule: f(a+b)=f(a)∗f(b)?
I found the easiest way to solve this by plugging values  let a=2 and b=3 So we will check whether f(2)*(f*3) = f(5)
There may be a better way to solve it
A. f(x)=x^2+1
f(2)=5 f(3)=10 f(5)=26 f(2)*f(3)=50
INCORRECT
B. f(x)=5^(2x) / 3
f(2)= 5^4/3 f(3)=5^6/3 f(5)=5^10/3 f(2)*f(3)=5^10/9
INCORRECT
C. f(x)=3x+2
f(2)=8 f(3)=11 f(5)=17 f(2)*f(3)=88
INCORRECT
D. f(x)=√2x
f(2)=√4 f(3)=√6 f(5)=√10 f(2)*f(3)=√24
INCORRECT
E. f(x)=24^x
f(2)=24^2 f(3)=24^3 f(5)=24^5 f(2)*f(3)=24^5
CORRECT
Answer: E



Manager
Joined: 06 Jun 2019
Posts: 114

Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
Updated on: 08 Jul 2019, 13:36
\(f(a+b)=f(a)∗f(b)\) means that \(f(5+5) = f(5) * f(5)\) or \(f(7+3) = f(7) * f(3)\) or etc. Let's check answer choices by plugging in numbers: A. Is \(f(x)=x^2+1\) true for \(f(5+5) = f(5) * f(5)\) ? \(f(5+5) = f(10) = 10^2+1 = 101\) \(f(5) = 5^2+1 = 26\) So the result of \(f(5+5) = f(5) * f(5)\) would be \({101}\neq{26+26}\). A is out. Plugging the same numbers in B, C, and D, we can see that they are incorrect. E. Is \(f(x)=24^x\) true for \(f(5+5) = f(5) * f(5)\) ? \(f(5+5) = f(10) = 24^{10}\) \(f(5) = 24^5\) So the result of \(f(5+5) = f(5) * f(5)\) would be \(24^{10} = 24^5*24^5\). Correct
Hence E
_________________
Bruce Lee: “I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times.”GMAC: “I fear not the aspirant who has practiced 10,000 questions, but I fear the aspirant who has learnt the most out of every single question.”
Originally posted by JonShukhrat on 08 Jul 2019, 08:50.
Last edited by JonShukhrat on 08 Jul 2019, 13:36, edited 3 times in total.




Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
08 Jul 2019, 08:50



Go to page
1 2 3 4 5
Next
[ 86 posts ]



