Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 27 Mar 2018
Posts: 79
Location: India

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 10:30
A. a^2+b^2+2ab+1 != a^2+b^2+2
B. 5^2(a+b)/3 != 5^2a/3 *5^2b/3 => 5^2(a+b)/9
C. 3(a+b)+2 != 3(a+b)+4
D. \(\sqrt{2(a+b)}\) != 2ab
E. 24^(a+b) = 24^a * 24^b => 24^(a+b)
So answer is E.



Manager
Joined: 10 Aug 2016
Posts: 68
Location: India

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 10:53
Which of the following function follows the rule: f(a+b)=f(a)∗f(b)
A. f(x)=x^2+1 f(a+b) = (a+b)^2 + 1 f(a)*f(b) = (a^2 + 1)*(b^2 + 1) clearly not equal. incorrect.
B. f(x)=(5^2x)/3 f(a+b) = (5^2(a+b))/3 f(a)*f(b) = (5^2a)/3 * (5^2b)/3 = (5^2(a+b))/9 Not equal. Incorrect.
C. f(x)=3x+2 f(a+b) = 3a + 3b +2 f(a)*f(b) = (3a+2)*(3b+2) Not equal. Incorrect.
D. f(x)=sqrt(2x) f(a+b) = sqrt(2(a+b)) f(a)*f(b) = sqrt(2a)*sqrt(2b) = 2*sqrt(ab) Not equal. Incorrect
E. f(x)=24^x f(a+b) = 24^(a+b) f(a)*f(b) = (24^a)*(24^b) = 24^(a+b). Equal. Correct.
Correct Answer: E



Intern
Joined: 06 Jul 2018
Posts: 31
Location: India

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 10:55
Correct Answer is E i.e. 24^x Question is f(a+b) = f(a).f(b) example 2+2 = 2*2 Now plug in 4 in each function and plug in 2 in each function and square the result Which ever option gives same answer is correct



Manager
Joined: 06 Feb 2019
Posts: 110

Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 11:04
Let a = 2 and b=3
24^5=24^2 * 24^3
The answer is E
Posted from my mobile device



Manager
Joined: 19 Apr 2017
Posts: 168
Concentration: General Management, Sustainability
GPA: 3.9
WE: Operations (Hospitality and Tourism)

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 11:05
f(a+b)=f(a)∗f(b)
30 seconds approach If you look at the answers and notice the Product Rule. it cut shorts the time The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents.
2 min approach:Solving using number picking lets assume a=2,b=2, a+b=4
f(a+b)=(4)^2+1 = 17 f(a)∗f(b)=(2^2+1)(2^2+1)=25 False
f(a+b)=[(5)^2*4]/3 = [5^8]/3 f(a)∗f(b)=[5^2*2]/3*[5^2*2]/3 False
f(a+b)=(4)+2 = 6 f(a)∗f(b)=(3(2)+2)(3(2)+2)=8*8 False
f(a+b)=√2*4=√8 f(a)∗f(b)=(√2*2)(√2*2)=√16 False
f(a+b)=\(24^4\) f(a)∗f(b)=\((24^2)*(24^2)=24^4\) TRUE
Answer E



Manager
Joined: 06 Aug 2018
Posts: 97

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 11:05
Definitely answer is E
The fight was between A and E
E is true in all.conditions
A fails at a=1 and b=1
So hence answer is definitely E
Posted from my mobile device



Director
Joined: 22 Nov 2018
Posts: 562
Location: India
GMAT 1: 640 Q45 V35 GMAT 2: 660 Q48 V33

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 11:11
It is obvious only option E will satisfy. Still the workings
A. f(x)=x^2+1 ; f(a+b) = (a+b)^2+1 and f(a)*f(b) = a^2*b^2 + a^2 + b^2 +1  Not Equal
B. f(x)=5^2x/3 ; f(a+b) = 5^2(a+b)/3 and f(a)*f(b) = 5^2(a)/3*5^(b)/3  Not Equal as denominator will be 9 C. f(x)=3x+2 ; f(a+b) = 3(a+b)+2 and f(a)*f(b) = 3(a+2)*3(b+2)  Not Equal
D. f(x)=√2x ; f(a+b) = √2(a+b) and f(a)*f(b) = 2√ab  Not Equal
E. f(x)=24^x ; f(a+b) = 24^(a+b) and f(a)*f(b) = 24^a*24^b=24^(a+b)  Equal
IMO E



Manager
Joined: 18 Jun 2013
Posts: 139
Location: India
Concentration: Technology, General Management
GPA: 3.2
WE: Information Technology (Consulting)

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 11:19
Which of the following function follows the rule: f(a+b)=f(a)∗f(b)?
Method 1: As per the rule that needs to be true, we can foresee that if the variable is in exponentials then a mere multiplication can simply lead to addition and the rule can hold true for the equation.
As per this, we see that the options 2 and 5 are the only ones where the variable is completely in the exponentials.
In option 2 the denominator will not allow the rule to hold true as in the RHS it will multiply. Hence option 2 is not correct.
In option 5, we have no other issues and the variable in the exponentials will simply add up on multiplication of the entities and hence the rule will always hold true.
Now, we can plug in some sample values and see if our analysis is correct and mark the correct answer which is option E.
Method 2: Putting values. This method is fool proof but may take you a couple of minutes to solve this question.
Option 1: f(x)=x^2+1
f(1 + 1) = f(1) = 1^2 + 1 = 5 f(1) = 1^2 + 1 = 2
If rule is true here then, f(1 + 1) = f(1) * f(1)
However, 5 <> 2
Hence, f(1 + 1) <> f(1) * f(1)
Option 1 is not correct.
Option 2: f(x) = (5^(2x))/3
f(1 + 1) = f(2) = (5^(2*2)) / 3 = (5^4) / 3 = 625/3 f(1) = (5^(2*1)) / 3 = 25/3
If rule is true here then, f(1 + 1) = f(1) * f(1)
625/3 = 25/3 * 25/3 > Rule holds here.
f(1 + 0) = f(1) = (5^(2*1)) / 3 = 25/3 f(1) = (5^(2*1)) / 3 = 25/3 f(0) = (5^(2*0)) / 3 = 1/3
However, 25/3 <> 25/3 * 1/3
Now, f(1 + 1) = f(1) * f(1); BUT, f(1 + 0) <> f(1) * f(0);
Hence, rule holds true sometimes but not always for this option.
Option 2 is not correct.
Option 3: f(x) = 3x + 2
f(1 + 1) = f(2) = 3*2 + 2 = 8 f(1) = 3*1 + 2 = 5
If rule is true here then, f(1 + 1) = f(1) * f(1)
However, 8 <> 5 * 5
Hence, f(1 + 1) <> f(1) * f(1)
Option 3 is not correct.
Option 4: f(x) = sqrt(2*x)
Consider, f(1 + 1) = f(2) = sqrt(2*2) = 2 f(1) = sqrt(2*1) = sqrt(2)
If rule is true here then, f(1 + 1) = f(1) * f(1)
And, 2 = sqrt(2) * sqrt(2)
Now consider, f(2 + 3) = f(5) = sqrt(2*5) = sqrt(10) f(2) = sqrt(2*2) = 2 f(3) = sqrt(2*3) = sqrt(6)
However, sqrt(10) <> 2 * sqrt(6)
Hence, f(1 + 1) <> f(1) * f(1)
Option 4 is not correct.
Option 5: f(x) = 24^x
Consider, f(1 + 1) = f(2) = 24^2 f(1) = 24^1
If rule is true here then, f(1 + 1) = f(1) * f(1)
And, 24^2 = 24^1 * 24^1
Consider, f(2 + 3) = f(5) = 24^5 f(2) = 24^2 f(3) = 24^3
If rule is true here then, f(1 + 1) = f(1) * f(1)
And, 24^5 = 24^2 * 24^3
Hence Option 5 or Option E is correct.



Senior Manager
Joined: 27 Aug 2014
Posts: 368
Location: Netherlands
Concentration: Finance, Strategy
GPA: 3.9
WE: Analyst (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, 11:20
Answer : E
substituting a+b once for x in E yields 24^(a+b) f(a)*f(b) = 24^aX24^b = 24^(a+b)
rest all equations yield different results. so E



Manager
Joined: 29 Nov 2018
Posts: 168

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 11:22
let a=1 b=2
E. f(a+b) = f(3)= 24^3 f (a) = 24 f (b) = 24^2 f (a) * f(b) = 24^3
IMO option E



Director
Joined: 18 May 2019
Posts: 530

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 11:54
f(a+b)=f(a)*f(b) We know that x^(a+b)={x^a}*{x^b}. The function in the answer choices that most resemble this property is E. So I will test for this option first. f(x)=24^x. f(a)=24^a and f(b)=24^b. f(a+b)=24^(a+b) f(a)*f(b)=(24^a)*(24^b) =24^(a+b). Hence the answer is E.
Posted from my mobile device



Director
Status: Manager
Joined: 27 Oct 2018
Posts: 748
Location: Egypt
Concentration: Strategy, International Business
GPA: 3.67
WE: Pharmaceuticals (Health Care)

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 12:16
for \(f(x)=x^2+1\): f(a+b) = \((a+b)^2 + 1 = a^2 + b^2 + 2ab + 1\) f(a)∗f(b) = \(a^2 + 1 + b^2 + 1 = a^2 + b^2 + 2\) > not equal for all values
for \(f(x)=\frac{5^{2x}}{3}\): f(a+b) = \(\frac{5^{2(a+b)}}{3} = \frac{5^{2a}5^{2b}}{3}\) f(a)∗f(b) = \(\frac{5^{2a}}{3}*\frac{5^{2b}}{3} = \frac{5^{2a}5^{2b}}{9}\)> not equal for all values
for \(f(x)=3x+2\): f(a+b) = \(3(a+b) + 2 = 3a + 3b + 2\) f(a)∗f(b) = \((3a+2)(3b+2) = 9ab + 6b + 6a + 4\) > not equal for all values
for f(x)= \(\sqrt{{2x}}\): f(a+b) = \(\sqrt{{2(a+b)}} = \sqrt{{2a+2b}}\) f(a)∗f(b) = \(\sqrt{{2a}}* \sqrt{{2b}} = \sqrt{{4ab}} = 2\sqrt{{ab}}\) > not equal for all values
for \(f(x)= 24^x\): f(a+b) = \(24^{a+b}\) f(a)∗f(b) = \(24^{a}*24^{b} = 24^{a+b}\) > equal
E



Manager
Joined: 01 Aug 2017
Posts: 220
Location: India
Concentration: General Management, Leadership
GPA: 3.4
WE: Information Technology (Computer Software)

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 12:20
Which of the following function follows the rule: f(a+b)=f(a)∗f(b)?
A. f(x)=\(x^2+1\)
B. f(x)=\(5^2^x * 3\)
C. f(x)=3x+2
D. f(x)=\(\sqrt{2x}\)
E. f(x)=\(24^x\)
A  f(a) = \(a^2 +1\) f(b) = \(b^2 +1\) f(a+b) = \((a+b)^2 +1\). f(a) * f(b) = \(a^2*b^2 +a^2+b^21\) Clearly f(a+b) is not equal to f(a)∗f(b).
B  f(a)=\(5^2^a * 3\) f(b)=\(5^2^b * 3\) f(a+b)=\(5^2^(a+b) * 3\). f(a) * f(b) = \(5^2^a+b * 9\) Clearly f(a+b) is not equal to f(a)∗f(b).
C  f(a)=\(3a+2\) f(b)=\(3b+2\) f(a+b)=\(3(a+b)+2\). f(a) * f(b) = \(9ab+6a+6b+4\) Clearly f(a+b) is not equal to f(a)∗f(b).
D  f(a)=\(\sqrt{2a}\) f(b)=\(\sqrt{2b}\) f(a+b)=\(\sqrt{2(a+b)}\) f(a)*f(b)=\(\sqrt{4ab}\) Clearly f(a+b) is not equal to f(a)∗f(b).
E  f(x)=\(24^x\)
f(a)=\(24^a\) f(b)=\(24^b\) f(a+b)=\(24^(a+b)\) f(a) * f(b)=\(24^(a+b)\). Clearly f(a+b) is equal to f(a)∗f(b)
Hence E



Senior Manager
Joined: 13 Feb 2018
Posts: 480

Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 13:28
GMAT likes to throw such questions to waste your precious time. It's not about concepts or clues, but about hard work on your pad. Per my experience, the first two options are definitely the wrong answer you have to sweat searching for correct option Let's begin A) \((a^2+1)*(b^2+1)=(a+b)^2+1\); at a glance on the left side, we will have \(a^2*b^2\) that is impossible for the right hand. NO B) \(5^{2a+2b}/9=5^{2a+2b}/3\); NO C) \((3a+2)*(3b+2)=3(a+b)+2\); NO D) \(\sqrt{4ab}=\sqrt{2a+2b}\) NO Last one hold the breath, otherwise you have to go back checking all the options once again E) \(24^a*24^b=24^{a+b}\) IMO Ans: E



Manager
Joined: 21 Jan 2019
Posts: 100

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 13:53
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+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 Here among all the options only in option e, f(a+b) = f(a) * f(b) as exponents add each other when multiplied. base wont matter here. Option E.



Manager
Joined: 29 May 2019
Posts: 122

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 15:27
Which of the following function follows the rule: f(a+b)=f(a)∗f(b)? We have to look for the option in which addition and multiplication might result in same value. If we look at the answer choices we can eliminate A, C and D easily. But to make sure we will put value of x and check.
A. f(x)=x^2+1 f(a+b)= (a+b)^2+1 f(a)*f(b) = (a^2 + 1)* (b^2+1) after solving we do not get similar values.B. f(x)=5^2x/3 f(a+b)=5^2(a+b)/3 f(a)*f(b)=5^2a/3* 5^2b/3 After solving this we get same numerator but different denominator.C. f(x)=3x+2 f(a+b)=3(a+b)+2 f(a)*f(b)=(3a+2)*(3b+2) after solving we do not get similar values.D. f(x)=sq root of 2x f(a+b)=sq root of 2(a+b) f(a)*f(b)=sq root of 2a * sq root of 2b after solving we do not get similar values.E. f(x)=24^x f(a+b)=24^(a+b) f(a)*f(b)=24^a* 24^b We get similar values on both sides. Correct.
_________________
Pick yourself up, dust yourself off, and start again.
Success is the sum of all small efforts.
MAKE IT HAPPEN



Senior Manager
Joined: 20 Mar 2018
Posts: 407
Location: Ghana
Concentration: Finance, Real Estate

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 16:31
f(a+b) = f(a) • f(b) So too many variables here let’s solidify it. let a= 1 , b=1 .: f(1+1) = f(1)•f(1) —> f(0)= f(1)•f(1)
(a) f(x) = x^2+1 f(0)= 0^2+1 =1 and f(1)•f(1)= f(1^2+1)•f(1^2+1) =4 So 1 is not equal to 2 (doesn’t follow rule)
(b) f(x)=((5)^2x)/3 f(0)=5^0/3 =1/3 and f(1)•f(1)=f(5^(2)/3)•f(5^2/3) = (1/3•25)•(25/3) =1/9 1/3 not equal to 1/9
(c) f(x) = 3x+2 f(0)=3(0)+2 =2 and f(1)•f(1)= f(3(1)+2)•f(3(1)+2)= 5 Doesn’t follow rule
(d) f(x) = (sqrt.2x) f(0)=( sqrt.2(0))= 0 and f(1)•f(1)= f(sqrt.2(1))•f(sqrt2(1)) =2i Doesn’t follow rule
(e) f(x) = 24^x f(0) = 24^0 = 1 and f(1)•f(1)= f(24^1)•f(24)= 1 1 equals 1 follows rule of f(0) = f(1)•f(1)
Answer E
Posted from my mobile device



Senior Manager
Joined: 12 Sep 2017
Posts: 308

Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 16:37
\(24^x\) where a = 2, b= 2.
\(f(a + b) = f(a) * f(b)\)
\(f(2 + 2) = f(2) * f(2)\)
\(4 = 4\)
For \(f(a + b)\)
\(24^4 = (3^4 * 2^12)\)
For \(f(a) * f(b)\)
\(24^2 * 24^2\)
\((2^6 * 3^2) * (2^6 * 3^2)\)
\((2^12 * 3^4)\)
E



Manager
Joined: 28 Jan 2019
Posts: 127
Location: Peru

Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 18:47
A. f(x)=x^2+1, if we replace, we have (a+b)^2 +1 ≠ (a^2+1)*(b^2 +1)
B. f(x)=5^2x/3, if we replace, we have 5^2(a+b)/3 ≠ (5^2a/3)*(5^2b/3)
C. f(x)=3x+2, if we replace, we have 3(a+b)+2 ≠ (3(a+2))*(3(b+2))
D. f(x)=√2x, if we replace, we have √2(a+b) ≠ √2a*√2b
E. f(x)=24x, if we replace, we have 24^(a+b) = 24^a*24^b
So (E) is our answer.



Intern
Status: Your greatest achievement lies in overcoming your biggest weakness.
Joined: 08 Jun 2019
Posts: 29
Location: India
GPA: 3.8
WE: Business Development (Consulting)

Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
Show Tags
08 Jul 2019, 20:01
IMO  E Because 24^x for f(a+b) = 24^(a+b) = 24^a*24^b for f(a)*f(b) = 24^a*24^b.
_________________
580  560  Hoping For the best




Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
[#permalink]
08 Jul 2019, 20:01



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



