GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 19 Jan 2020, 12:59

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

Hide Tags

Manager
Joined: 30 Nov 2017
Posts: 194
WE: Consulting (Consulting)
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

Show Tags

08 Jul 2019, 08:55

Posted from my mobile device
_________________
Be Braver, you cannot cross a chasm in two small jumps...
BSchool Moderator
Joined: 07 Dec 2018
Posts: 160
Location: India
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

Show Tags

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
Joined: 12 Mar 2018
Posts: 83
Location: United States
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

Show Tags

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
Senior Manager
Joined: 04 Apr 2015
Posts: 254
GMAT 1: 650 Q49 V31
GPA: 3.59
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

Show Tags

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
SC Moderator
Joined: 25 Sep 2018
Posts: 605
Location: United States (CA)
Concentration: Finance, Strategy
GPA: 3.97
WE: Investment Banking (Investment Banking)
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

Show Tags

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.
_________________
Why do we fall?...So we can learn to pick ourselves up again
Intern
Joined: 17 Jun 2019
Posts: 18
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

Show Tags

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
_________________
“Failure is success if we learn from it.”
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)   [#permalink] 10 Jul 2019, 21:36

Go to page   Previous    1   2   3   4   5   [ 86 posts ]

Display posts from previous: Sort by