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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Which of the following function follows the rule: f(a + b) = f(a)*f(b)

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Intern  S
Joined: 24 Mar 2018
Posts: 48
Location: India
Concentration: Operations, Strategy
GMAT 1: 620 Q48 V28 GMAT 2: 680 Q49 V34 GMAT 3: 710 Q49 V38 WE: Project Management (Energy and Utilities)
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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A. f(x)=$$x^2$$+1

f(a+b) = $$a^2$$+$$b^2$$+2ab+1
f(a).f(b) = $$a^2$$$$b^2$$+$$a^2$$+$$b^2$$+1

Not equal

B. f(x)=$$5^{2x}$$/3

f(a+b) = $$5^{2a+2b}$$/3
f(a).f(b) = $$5^{2a+2b}$$/9

Not equal

C. f(x)=3x+2

f(a+b) = 3a+3b+2
f(a).f(b) = (3a+2)(3b+2)

Not equal

D. $$f(x)=\sqrt{2x}$$

$$f(a+b) = \sqrt{2(a+b)}$$
$$f(a).f(b) = 2\sqrt{ab}$$

Not equal

E. f(x)=$$24^x$$

f(a+b) = $$24^{a+b}$$
f(a).f(b) = $$24^{a+b}$$

Equal

Hence, option E.
Manager  S
Joined: 17 Apr 2018
Posts: 107
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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To narrow down on the choice we need to focus on the possible option.

Ditching A and C for the timebeing as they contain the constant value. ==> not eliminating but choosing best option to plug in values.

Down to B, D and E

breaking F(x) = f(x/2 + x/2)

only option E satisfies.

Intern  B
Joined: 09 Mar 2019
Posts: 11
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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for option E: f(a) * f(b) = 24^a * 24 ^b = 24^(a+b)

f(a+b) = 24^(a+b)

Hence IMO ans is E
Manager  S
Status: Victory is never a one time thing.
Joined: 14 Jan 2018
Posts: 57
Location: Oman
Concentration: Marketing, Entrepreneurship
GMAT 1: 590 Q49 V21 GMAT 2: 650 Q47 V33 GPA: 3.8
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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Here, f(x+x)= f(2x)
Therefore, f(x)*f(x) must equal f(2x)

Working in reverse from the answers (which I figured has to be the easiest approach), I decided to start with option D as I instinctively felt there has to be a relation between the square root in this option and the squared f(x) in question.

f(x)*f(x)= root of (4(square of x)) = 2x
f(2x)= 2(root of x)

Hence wrong.

Consider option E.

f(x)*f(x)= 24 power x * 24 power x which is equal to 24 power 2x.
f(2x) also equals 24 power 2x.

Hence E is the correct option.
Senior Manager  V
Joined: 25 Sep 2018
Posts: 468
Location: United States (CA)
Concentration: Finance, Strategy
GMAT 1: 640 Q47 V30 GPA: 3.97
WE: Investment Banking (Investment Banking)
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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Which of the following function follows the rule: f(a+b)=f(a)∗f(b)f(a+b)=f(a)∗f(b)?

In this we have to replace x with (a+b) in LHS, and a & b separately in place of x in RHS, we have to stick to the fucnction given in the option.

A. If we solve the equation, we get that LHS is not equal to RHS hence incorrect.

B. LHS is not equal to RHS

C. LHS is not equal to RHS

D. LHS is not equal to RHS

E. LHS is equal to RHS and hence is the correct answer, Important part here is, we have to properly substitute the values.
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Why do we fall?...So we can learn to pick ourselves up again
Intern  B
Joined: 17 Jun 2019
Posts: 18
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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put a =0;
$$f(b) = f(0)*f(b)$$
Hence $$f(0)$$ has to be 1

This will limit the options to A and E for which you can solve the equations and get E as the answer
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“Failure is success if we learn from it.” Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)   [#permalink] 10 Jul 2019, 21:36

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