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Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
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08 Jul 2019, 08:51
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)
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08 Jul 2019, 08:51
Answer is E. 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)
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08 Jul 2019, 08:53
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)
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Updated on: 08 Jul 2019, 22:51
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, 08:54.
Last edited by mira93 on 08 Jul 2019, 22:51, 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)
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08 Jul 2019, 08:55
Looking at the options my answer choice is Answer Choice A. 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)
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08 Jul 2019, 08:56
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)
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08 Jul 2019, 09:03
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)
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08 Jul 2019, 09:03
Correct option is E
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Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
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08 Jul 2019, 09:08
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)
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08 Jul 2019, 09:09
IMOE
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)
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Updated on: 08 Jul 2019, 09:21
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, 09:15.
Last edited by Kinshook on 08 Jul 2019, 09:21, 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)
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08 Jul 2019, 09:16
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)
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08 Jul 2019, 09:21
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)
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08 Jul 2019, 09:43
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)
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08 Jul 2019, 09:45
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
Answer is E
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)
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08 Jul 2019, 09:57
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)
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08 Jul 2019, 09:59
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.
(B) is the answer.



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Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
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08 Jul 2019, 10:02
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)
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08 Jul 2019, 10:05
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)
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08 Jul 2019, 10:21
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.
Hence the answer is E.
Please hit kudos if you like the solution.




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