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Which of the following function follows the rule: f(a + b) = f(a)*f(b)
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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. \(f(x)= 24^x\)
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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, 07:08
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)
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08 Jul 2019, 07:14
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)
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08 Jul 2019, 07:17
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)
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08 Jul 2019, 07:22
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)
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08 Jul 2019, 07:24
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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Which of the following function follows the rule: f(a + b) = f(a)*f(b)
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Updated on: 09 Jul 2019, 00:54
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, 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)
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08 Jul 2019, 07:31
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)
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08 Jul 2019, 07:32
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)
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08 Jul 2019, 07:36
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)
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08 Jul 2019, 07:37
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)
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08 Jul 2019, 07:38
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)
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08 Jul 2019, 07:44
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)
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08 Jul 2019, 07:46
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)
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08 Jul 2019, 07:47
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)
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Updated on: 08 Jul 2019, 12:36
\(f(a+b)=f(a)∗f(b)\) 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)
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08 Jul 2019, 07:51
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, 07:51
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, 07:53
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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Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)
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08 Jul 2019, 08:03
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)
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