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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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08 Jul 2019, 07:00
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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. $$f(x)= 24^x$$

 This question was provided by e-GMAT for the Game of Timers Competition

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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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08 Jul 2019, 07:08
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2
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
##### General Discussion
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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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08 Jul 2019, 07:14
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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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08 Jul 2019, 07:17
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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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08 Jul 2019, 07:22
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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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08 Jul 2019, 07:24
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)
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Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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Updated on: 09 Jul 2019, 00:54
3
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)

Posted from my mobile device

Originally posted by prashanths on 08 Jul 2019, 07:31.
Last edited by prashanths on 09 Jul 2019, 00:54, 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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08 Jul 2019, 07:31
2
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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08 Jul 2019, 07:32
2
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.

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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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08 Jul 2019, 07:36
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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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08 Jul 2019, 07:37
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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

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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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08 Jul 2019, 07:38
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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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08 Jul 2019, 07:44
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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

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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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08 Jul 2019, 07:46
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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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08 Jul 2019, 07:47
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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

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

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Updated on: 08 Jul 2019, 12:36
2
$$f(a+b)=f(a)∗f(b)$$ 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, 07:50.
Last edited by JonShukhrat on 08 Jul 2019, 12:36, edited 3 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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08 Jul 2019, 07:51
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The correct answer is E, because

24^(a+b)=(24^a)*(24^b)
24^(a+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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08 Jul 2019, 07:51
2
A=2; b=3; a+b=5

e) f(x)=24x
24ˆ5= 24ˆ2+24ˆ3=2+3=5
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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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08 Jul 2019, 07:53
1
IMO E

1: let x=1,b=2
f(a+b)=(1+2)^2+1=10,
f(a)+f(b)=(1+1)+( 4+1)=7 so this option is wrong

2:let a=0 and b=1
(5^2(1))/3 not eqaul to (5^2(0))/3 + (5^2(1))/3
wrong

3: let a=0 and b=1
(3(0)+2)+(3(1)+2)=7
and 3(1)+2=5
and so this option is also wrong

4:let a=1 and b=2
root(2(1))+root(2(2))=2+root(2)
root(2)(3)=root(6)

so f(a+b) not equal to f(a)+(b) and this option is wrong for this reason.

5:let a=1 and b=2
(24)^(3)=24^1*24^2

Option E is the correct 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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08 Jul 2019, 08:03
2
by just looking at equations and substituiting
2and 3 for a& b

24^5=24^2*24^3=24^(2+3)

option E
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)   [#permalink] 08 Jul 2019, 08:03

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