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

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

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New post 08 Jul 2019, 08:00
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A
B
C
D
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 08 Jul 2019, 08:08
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1
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
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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 08 Jul 2019, 08:12
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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)
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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 08 Jul 2019, 08:14
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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)
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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 08 Jul 2019, 08:17
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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
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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 08 Jul 2019, 08:22
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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
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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 08 Jul 2019, 08:23
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E.

f(a+b) = 24^(a+b)
f(a)*f(b) = 24^a*24^b = 24^(a+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 08 Jul 2019, 08:24
2
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.
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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 08 Jul 2019, 08:26
E is the correct answer as powers of 24 will add.

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

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New post Updated on: 09 Jul 2019, 01:54
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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.

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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.
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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 08 Jul 2019, 08:31
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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.
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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 08 Jul 2019, 08:32
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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)
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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 08 Jul 2019, 08:36
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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
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Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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New post 08 Jul 2019, 08:37
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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
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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 08 Jul 2019, 08:38
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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
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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 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.
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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 08 Jul 2019, 08:44
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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
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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 08 Jul 2019, 08:46
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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)
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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 08 Jul 2019, 08:47
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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
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Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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New post Updated on: 08 Jul 2019, 13:36
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\(f(a+b)=f(a)∗f(b)\) 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
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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.
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Which of the following function follows the rule: f(a + b) = f(a)*f(b)   [#permalink] 08 Jul 2019, 08:50

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