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

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Manager
Joined: 30 Nov 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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08 Jul 2019, 08:55

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, 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.

Manager
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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, 23:34
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
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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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09 Jul 2019, 00:17
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
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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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09 Jul 2019, 07:54
Which of the following function follows the rule: f(a+b)=f(a)∗f(b)f(a+b)=f(a)∗f(b)?

In this we have to replace x with (a+b) in LHS, and a & b separately in place of x in RHS, we have to stick to the fucnction given in the option.

A. If we solve the equation, we get that LHS is not equal to RHS hence incorrect.

B. LHS is not equal to RHS

C. LHS is not equal to RHS

D. LHS is not equal to RHS

E. LHS is equal to RHS and hence is the correct answer, Important part here is, we have to properly substitute the values.
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Joined: 17 Jun 2019
Posts: 18
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

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10 Jul 2019, 21:36
put a =0;
$$f(b) = f(0)*f(b)$$
Hence $$f(0)$$ has to be 1

This will limit the options to A and E for which you can solve the equations and get E as the answer
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Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)   [#permalink] 10 Jul 2019, 21:36

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