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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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08 Jul 2019, 07:51
2
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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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, 21:51
1
Answer is E. For such questions, I try to plug in values. a=5, b=5.
Only E will yield the same result in both sides. 24^10=$$24^5$$*$$24^5$$=24^10=24^10(5+5). Even if a is 3, and b is 7, $$24^3$$*$$24^7$$=24^3+7=24^10

Originally posted by mira93 on 08 Jul 2019, 07:54.
Last edited by mira93 on 08 Jul 2019, 21:51, edited 4 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, 07:55

Posted from my mobile device
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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, 07:56
1
IMO E

Assume values a=2 and b=3
Hence, f(5) = f(2)*f(3)

Now, substitute x=2,3 and 5 in all the options.
Only for option E, LHS = RHS.

f(2) = 24^2
f(3) = 24^3
f(5) = 24^5

Hence, f(2)*f(3) = 24^2*24^3 = 24^5 = f(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, 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
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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
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Correct option 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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08 Jul 2019, 08:08
1
IMO E.

f(a+b)=f(a)∗f(b).
Let's consider a=2 and b=3 for all the options.

1. f(x)=x^2+1
f(2)= 5 and f(3) = 10. f(2+3)= 26 =/= 50. Incorrect option.

2. f(x)=5^(2x)/3
f(2)= 5^(4)/3 and f(3)= 5^(6x)/3. f(5) = 5^(10x)/3 =/= 5^(10x)/9. Incorrect option.

3. f(x)=3x+2
f(2)= 8, f(3)= 11, f(5)=17 =/= 88. Incorrect option.

4. f(x)=√2x
f(2)= 2, f(3)= √6, f(5)= √10 =/= 2√6. Incorrect option.

5. f(x)=24^x.
f(2) =24^2 , f(3)=24^3, f(5) = 24^5 ==24^5. 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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08 Jul 2019, 08:09
1
IMO-E

Rule: f(a+b)=f(a)∗f(b)f(a+b)=f(a)∗f(b)?

Pre Thinking- For fn f(x)=a^x , f(a+b)=f(a)*f(b)..A/c Ans E

However , if we don't know that lets try by putting values.
Assume a=1, b=2

A. f(x)=x^2+1
f(2)=5, f(3)=10, f(2+3)=26
Clearly, f(2+3)=26 not equals f(1)*f(2)=50

B. f(x)=5^2x/3
f(3)=5^6/3, f(2)=5^4/3, f(2+3)=5^10/3
Clearly, f(2+3)=5^10/3 not equals f(1)*f(2)=5^10/9

Similarly for C & D , f(2+3) not = f(2)*f(3)

E.f(x)=24^x
f(2)=24^2, f(2)=24^3, f(2+3)=24^5
f(2+3) = f(2)*f(3)
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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, 08:21
1
Which of the following function follows the rule: f(a+b)=f(a)∗f(b)

$$A. f(x)=x^2+1$$
$$f(a+b)= (a+b)^2+1$$
$$f(a)= a^2+1$$
$$f(b)= b^2+1$$
$$f(a).f(b)= (a^2+1)(b^2+1)$$
f(a+b)<>f(a).f(b)

B. f(x)=5^2x/3
f(a+b)= 5^2(a+b)/3
f(a)= 5^2a/3
f(b)=5^2b/3
f(a).f(b)= 5^2(a+b)/9
f(a+b)<>f(a).f(b)

C. f(x)=3x+2
f(a+b)= 3(a+b)+2 = 3a+3b+2
f(a)= 3a+2
f(b)= 3b+2
f(a).f(b)= (3a+2)(3b+2) = 9ab+6b+6a+4
f(a+b)<>f(a).f(b)

$$D. f(x)=\sqrt{2x}$$
$$f(a+b)= \sqrt{2(a+b)}$$
$$f(a)=\sqrt{2a}$$
$$f(b)=\sqrt{2b}$$
$$f(a).f(b)=2\sqrt{ab}$$
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
f(a).f(b)=24^a.24^b = 24^(a+b) = f(a+b)

IMO E

Originally posted by Kinshook on 08 Jul 2019, 08:15.
Last edited by Kinshook on 08 Jul 2019, 08:21, 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, 08:16
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A. f(x)=x^2+1
(a+b)^2+1 is not equal to (a^2+1)(b^2+1)

B. f(x)=(5^2x) /3
(5^2(a+b)) /3 is not equal to (5^2a) /3 * (5^2b) /3

C. f(x)=3x+2
3(a+b)+2 is not equal to (3a+2)(3b+2)

D. f(x)=√2x
√2(a+b) is not equal to √2a*√2b

E. f(x)=24^x
24^(a+b) = 24^a*24^b (as we know when bases are same powers gets added)

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, 08:21
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Hit and try in options in E 24^x * 24*y = 24 (x+y)
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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, 08:43
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f(a+b)= f(a) ∗ f(b)

Using option (e)

$$24^(a+b)$$= $$24^a$$ * $$24^b$$. which satisfies.

IMO. (e) is the right 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, 08:45
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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)?

A. f(x)=x2+1

B. f(x)=52x3

C. f(x)=3x+2f(x)=3x+2

D. f(x)=2x‾‾√f(x)=2x

E. f(x)=24x

f(a+b) should be equal to f(a)*f(b)

Lets take choice E - f(x) = 24^x
F(a+b) = 24^(a+b)
f(a) * f(b) = 24^a * 24^b = 24^(a+b). Similarly we can do this type of expansion for all choices.
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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, 08:57
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Substitute x = a+b for F(a+b) in F(x) and x=a for f(a) in f(x) and x=b for f(b) in f(x) and multiply to check both match

E matches

also we can immediately notice that a^x * a^y = a^(x+y) hence 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, 08:59
f(a+b)=f(a)∗f(b)

Let's see each option :

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

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

Hence the rule is NOT followed here.
So, the first option is OUT.

2.)
f(x) = $$5^\frac{2x}{3}$$
f(a)=$$5^\frac{2a}{3}$$
f(b)=$$5^\frac{2b}{3}$$
f(a+b) = $$5^\frac{2(a+b)}{3}$$ = f(a)*f(b)

Hence the rule is followed here.

We don't need to check further.

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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, 09:02
1
f(a+b)=f(a)∗f(b)

this type of function is possible in exponents

A. f(x)=x^2+1
f(a+b) is not equal to f(a)∗f(b)

B. f(x)=5^2x/3
f(a+b) is not equal to f(a)∗f(b)

C. f(x)=3x+2
f(a+b) is not equal to f(a)∗f(b)

D. f(x)=√2x
f(a+b) is not equal to f(a)∗f(b)

E. f(x)= 24^x ===> clearly 24^(a+b) = 24^a * 24^b - Correct
f(a+b) is equal to 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, 09:05
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for this question, simply plug in a value.
Let's take a=2, b=3

following this equation, f(5) = f(2) * f(3), we evaluate each answer choices.

a. 26 != 50
b. 5^10/3 != 5^10/9
c. 17 != 88
d. sqrt 10 != sqrt 24
e. 24^5 = 24^5

e, wins
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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, 09:21
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The question is saying that, if we substitute the value of the function, then both side should we equal.

1. f(x)=x^2+1
f(a+b) = f(a) * f(b)
$$(a+b)^2$$ +1 = ($$a^2$$ +1) * ($$b^2$$ +1)
upon solving we can get that both sides are not equal.

2. $$\frac{(5^{2x})}{(3)}$$
$$\frac{(5^{2(a+b)})}{(3)}$$ = $$\frac{(5^{2a})}{(3)}$$* $$\frac{(5^{2b})}{(3)}$$
Both sides are not equal.

3. 3x+2
3(a+b) +2 = (3a +2) * (3b +2)
Not equal.

4. 2x
$$\sqrt{2(a+b)}$$= $$\sqrt{2a}$$ * $$\sqrt{2b}$$
Not Equal.

5. $$24^x$$
$$24^{a+b}$$ = $$(24^a)$$ * $$(24 ^b)$$
The both side for this equation are equal, as per the indices property.

Please hit kudos if you like the solution.
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)   [#permalink] 08 Jul 2019, 09:21

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