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Manager  G
Joined: 08 Jan 2018
Posts: 129
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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We need to check every option whether they satisfy.

A. $$f(x) = x^2 + 1$$
So,
$$f(a + b) = (a + b)^2 + 1 = a^2 + 2ab + b^2 + 1$$
$$f(a) * f(b) = (a^2 + 1) * (b^2 + 1) = a^2 + b^2 + a^2b^2 + 1$$
Clearly f(a + b) Not Equal to f(a)*f(b)

Similarly, it will not satisfy for options B, C, D

E. $$f(x) = 24^x$$

$$f(a + b) = 24^{a + b} = 24^a*24^b$$
$$f(a) * f(b) = 24^a*24^b$$
So, f(a + b) = f(a) * f(b)
Satisfies.

Manager  G
Joined: 25 Mar 2018
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GMAT 1: 640 Q50 V26 GMAT 2: 640 Q50 V26 GMAT 3: 650 Q50 V28 GMAT 4: 690 Q50 V31 GMAT 5: 730 Q50 V40 GPA: 4
WE: Analyst (Manufacturing)
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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this is substitution kind of question. Just substitute each answer choice with a+b and find if we get the output of f(a).f(b).

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

f(a+b) = (a+b)^2 + 1, f(a). f(b) = (a^2 + 1). (b^2 +1). clearly both are not equal.

B. f(x)=5^2x/3

similarly, f(a+b)=5(a+b)^2/3, f(a).f(b) = 5^2a/3 . 5^2b/3
both are not equal.

C. f(x)=3x+2

f(a+b) = 3(a+b) + 2 , f(a). f(b) = (3a+2).(3b+2). these exp are also not same.

D. f(x)=√2x

f(a+b) = √2(a+b). f(a).f(b) = √2(a).√2(b), which are not equal.

E. f(x)=24^x
f(a+b) = 24^(a+b)= (24^a). (24^b) = f(a).f(b). Hence the answer.

Correct choice is E
Manager  G
Joined: 15 Jun 2019
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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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take a =1, b=1

A. f(x)=x^2+1 gives 5 and 4 hence wrong

B. f(x)=5^2 * x/3 gives different ans hence wrong

C. f(x)=3x+2 gives 8 and 25 hence wrong

D. f(x)=\sqrt{2x} gives 2 and 2 hence keep

E. f(x)=24^x gives 24^2 and 24^2 hence keep

now substitute 1 and 4 for d and e

d) gives \sqrt{10} and 4 hence wrong

e) gives 24 ^5 and 24 ^5. hence e is answer
Manager  G
Joined: 17 Jul 2014
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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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f(a+b) = f(a) * f(b)

A. f(x)=x^2+1
replace LHS f(x) = f(a+b) RHS - (a+b)^2 + 1
RHS f(a) = a^2 & f(b) = b^2 -> RHS is not equal to LHS

B. f(x)=5^2 / 3
LHS f(a+b) = 5 (a+b)^2 / 3
RHS f(a) = 5a^2/3 f(b) = 5b^2/3
not equal

C. f(x)=3x+2
f(a+b) = 3(a+b)+2
f(a) * f(b) = (3a+2) (3b+2)

D. f(x)=√2x‾‾
f(a+b) = √2(a+b)‾‾
f(a) = √2a‾‾ + √2b‾‾ = √2‾‾ (√a‾‾ + √b‾‾ )
not equal

E. f(x)=24^x
f(a+b) = 24^(a+b)
f(a) * f(b) = 24^a * 24^b = 24^(a+b)

finally a match , E Intern  B
Joined: 05 Jul 2019
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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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F(a+b)= f(a)*f(b)
F(a+b)= 24^x * 24^x = F(a)*f(b)

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Intern  B
Joined: 08 Jul 2019
Posts: 37
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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Only E if we subsitute yeilds equality between both sides. We can plug in numbers to see if this is true. Pick easy numbers to work with, such that a=5, b=5 OR a=2, b=8.
E. 24^10=24^5*24^5=24^5+5=24^10.
OR 24^10=24^2*24^8=24^10.
Wer can go ahead and try substituting values for other questions, but none will work, I checked.
Thus E
Intern  B
Joined: 10 Jul 2018
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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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by option verification method we can substitute the values i.e f(x)=24power x
24 power(a+b)=24 power a*24 power b
since bases are powers must be added it becomes 24 power(a+b) .
Intern  B
Joined: 28 Feb 2018
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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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by putting a values a=2 , b=1 we can eliminate option C,D.

Thn put value a=3,b=2 we can eliminate option A,B.

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Joined: 20 Jul 2017
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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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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

Pls Hit Kudos if you like the solution
Manager  G
Joined: 12 Jan 2018
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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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(A)f(x)=$$x^{2}+1$$
f(x+1)=$$(x^{2}+2x+1)+1$$
f(1)=2
Clearly $$f(x+1)\neq f(x)*f(1)$$

(B)f(x)=$$\frac{5^{2x}}{3}$$
f(x+1)=$$\frac{5^{2(x+1)}}{3}$$ =$$\frac{5^{2(x)}}{3}$$ *5
f(1)=$$\frac{5^{2(1)}}{3}$$
Clearly $$f(x+1)\neq f(x)*f(1)$$
But this choice tells us that, had there been no coefficient (1/3) this choice would have been correct. So we are looking for choice, which has x in the power, and there are no co-efficient/constants multiplied to the base.
Since, $$a^{x+y}$$ =$$a^{x}*a^{y}$$

Glancing through other options, E is the correct answer.
_________________
"Remember that guy that gave up?
Neither does anybody else"
Manager  S
Joined: 24 Jan 2019
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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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Here, we can just put different values for a and b verify. (simple way)

(A) Here, +1 in the function will create issue when doing f(a)*f(b).

(B) 3 in the denominator will create issue when doing f(a)*f(b).

(C) + 2 in the function will create issue here.

(D) square root of x and 2x will differ by factor of 1.4 (root 2). (try putting a and (a+a). So, f(a)*f(a) is not equal to f(2a)).

(E) this function follows the given property.

Manager  S
Joined: 12 Mar 2018
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Location: United States
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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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)?

This one is easy because when you are looking for multiplication of two quantities to be equal to the addition of those two quantities, think about 1.
In this case, the very first answer choice has something to do with 1, so if we evaluate that, we can see that it satisfies the rule in the question.

x^2 + 1 = x^2 * 1
Intern  B
Joined: 09 May 2019
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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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Suppose a = 2 and b = 3
Then f(a+b) = f(5)

Only option E is correct and satisfies the Equality f(a+b) = f(a) * f(b)
when we put the values of a and b
f(a)= f(2) = 24^2
f(b) = f(3) = 24^3
f(a+b) = f(5) = 24^5
f(a)*F(b) = f(2) *f(3) = (24^2)*(24^3)= 24^5
Senior Manager  G
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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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Which of the following function follows the rule: f(a+b)=f(a)∗f(b)f(a+b)=f(a)∗f(b)?

this question can eat up your time a lot if you don't find a pattern
A. f(x)=x^2+1 : plug in
F(x)= f(A+B)= (A+B)^2
f(A)*f(B)= (A)^2 *B^2 : not equal no notice that we have AxB on one side and A+B on other to equalize them we need A and B in power : hints of A^n x A^r= A(n+r)

B. f(x)=(5^2x)/3 hold

C. f(x)=3x+2: eliminate x not in power

D. f(x)=(2x)^.5: eliminate not in power

E. f(x)=24^x:hold

plug A and B again
E first as its easier : f(A+B) :24^A+B , f(A)*f(B) = 24^(A) *24^(B) both are equal so E

no need to check B
Senior Manager  D
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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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Which of the following function follows the rule: f(a+b)=f(a)∗f(b)?

Let us try a=1, b=3, a+b= 1+3 = 4

A. f(x)=x^2+1
- f(a+b)=f(4)=17
- f(a)=f(1)=2, f(b)=f(3)=10, then f(a)∗f(b)= f(1)∗f(3) = 20
- the above function does NOT follow the rule: f(a+b)=f(a)∗f(b)

B. f(x)=5^(2x)/3
- f(a+b)=f(4)=(5^8)/3
- f(a)=f(1)=(5^2)/3, f(b)=f(3)=(5^6)/3, then f(a)∗f(b)= f(1)∗f(3) = (5^8)/9
- The above function does NOT follow the rule: f(a+b)=f(a)∗f(b)

C. f(x)=3x+2
- f(a+b)=f(4)=14
- f(a)=f(1)=5, f(b)=f(3)=11, then f(a)∗f(b)= f(1)∗f(3) = 55
- the above function does NOT follow the rule: f(a+b)=f(a)∗f(b)

D. f(x)=√(2x)
- f(a+b)=f(4)=√8
- f(a)=f(1)=√2, f(b)=f(3)=√6, then f(a)∗f(b)= f(1)∗f(3) = √12
- the above function does NOT follow the rule: f(a+b)=f(a)∗f(b)

E. f(x)=24^x
- f(a+b)=f(4)=24^4
- f(a)=f(1)=24^1, f(b)=f(3)=24^3, then f(a)∗f(b)= f(1)∗f(3) = 24^4
- the above function does follow the rule: f(a+b)=f(a)∗f(b)

Intern  B
Joined: 28 Jun 2019
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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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Option E is the right answer. f(a+b)=24^(a+b)=(24^a)*(24^b)=f(a)*f(b)

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Intern  B
Joined: 31 Jul 2018
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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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Here we can apply POE:

A. f(a)=a^2+1, f(b)=b^2+1,
f(a+b) =(a+b)^2+1 = (a^2+1)*(b^2+1) => WRONG

B. f(a)=5^2a/3, f(b)=5^2b/3
f(a+b)=5^2(a+b)/3=5^2(a+b)/3*3 => WRONG

C. f(a)=3a+2, f(b)=3b+2
f(a+b) = 3(a+b)+2 = (3a+2)*(3b+2)

D. f(a)=√2a, f(b)=√2b
f(a+b)=√2(a+b)=√4ab => WRONG

E. f(a)=24^a, f(b)=24^b
f(a+b)=24^(a+b)=24^a*24^b=24^(a+b) => RIGHT

Manager  B
Joined: 07 Jul 2019
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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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A) f(a+b)=(a+b)^2+1=(a^2+1)*(b^2+1)
a^2+2ab+b^2+1=a^2b^2+a^2+b^2+1
2ab does NOT equal to a^2b^2 (NO)
B) (5^2a+2b)/3=(5^2a)/3*(5^2b)/3
(5^2a+2b)/3 does NOT equal (25^2a+2b)/9. OUT
C) 3(a+b)+2=(3a+2)(3b+2)
3a+3b+2=9ab+6a+6b+4
0 does NOT equal 9ab+3a+3b+2. OUT
D)sqr root 2(a+b)=sqr root 2a*sqr root 2b
sqrt 2a+2b does NOT equal sqrt 4ab. OUT
E) 24^a+b=24^a*24^b
24^a+b=24^a+b. YES, this is answer (E)
Manager  S
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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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when we substitute the value in E
$$24^a*24^b$$=f(a+b)
in no other case this function is same. So option E is correct
Manager  S
Joined: 01 Oct 2018
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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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Which of the following function follows the rule: f(a+b)=f(a)∗f(b)?

We can bruteforce this question by input a sample or imagine a smarter way.
What operation a+b is given to us by a*b. It reminds me about power.
x^(a+b) = (x^a)*(x^b)
So let's check first of all powers, that is variants B and E.
E seems the easiest one, so let's start from E.
Sample a = 2 , b =3
E. 24^(5) = (24^3)*(24^2) True

Amsw is E Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)   [#permalink] 09 Jul 2019, 03:19

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