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

Question

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

shridhar786 · Accepted Answer

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

prashanths · Answer

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.

Posted from my mobile device

hiranmay · Answer

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)

ruchik · Answer

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

Archit3110 · Answer

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

lacktutor · Answer

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.

simpersome · Answer

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.

exc4libur · Answer

(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)

RJ7X0DefiningMyX · Answer

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

globaldesi · Answer

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

nick1816 · Answer

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

umarovaalbina · Answer

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

rahaman26 · Answer

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)

Vinit1 · Answer

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

JonShukhrat · Answer

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}
eq{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

CareerGeek · Answer

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 = a^2 + b^2 + 2ab + 1 
 f(a)*f(b) = (a^2+1)*(b^2+1) = (ab)^2 + a^2 + b^2 + 1  -->  NO

B.  f(x) = \frac{5^{2x}}{3} 
 f(a + b) = \frac{5^{2(a + b)}}{3} = \frac{5^{2a + 2b}}{3} 
 f(a)*f(b) = \frac{5^{2a}}{3}*\frac{5^{2b}}{3} = \frac{5^{2a + 2b}}{9}  -->  NO

C.  f(x) = 3x + 2 
 f(a + b) = 3(a + b) + 2 = 3a + 3b + 2 
 f(a)*f(b) = (3a + 2)*(3b + 2) = 9ab + 6a + 6b + 4  -->  NO

D.  f(x) = 2x 
 f(a + b) = 2(a + b) = 2a + 2b 
 f(a)*f(b) = 2a*2b = 4ab  -->  NO

E.  f(x) = 24^x 
 f(a + b) = 24^{a + b} 
 f(a)*f(b) = 24^a*24^b = 24^{a + b}  -->  YES

IMO Option E

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

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