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

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Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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New post 09 Jul 2019, 04:48
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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.
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Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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New post 09 Jul 2019, 06:02
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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.

Hence, E is the answer.
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Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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New post 09 Jul 2019, 06:36
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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
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Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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New post 09 Jul 2019, 07:26
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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.
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Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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New post 09 Jul 2019, 07:54
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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Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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New post 10 Jul 2019, 21:36
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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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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