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For which of the following functions f(x) is f(a + b) = f(a) ?

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For which of the following functions f(x) is f(a + b) = f(a) ?  [#permalink]

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New post 31 Jul 2018, 00:31
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For which of the following functions f(x) is \(f(a + b) = f(a) + f(b)\)?


(A) \(f(x) = x^2\)

(B) \(f(x) = 5x\)

(C) \(f(x) = 2x + 1\)

(D) \(f(x) =\sqrt{x}\)

(E) \(f(x) = x - 2\)

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Re: For which of the following functions f(x) is f(a + b) = f(a) ?  [#permalink]

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New post 31 Jul 2018, 01:32
Bunuel wrote:
For which of the following functions f(x) is \(f(a + b) = f(a) + f(b)\)?


(A) \(f(x) = x^2\)

(B) \(f(x) = 5x\)

(C) \(f(x) = 2x + 1\)

(D) \(f(x) =\sqrt{x}\)

(E) \(f(x) = x - 2\)


Instead of trying to work with the equations, we'll pick easy numbers to eliminate incorrect answers.
This is an Alternative approach.

Say a = 1 and b = 1, so a+b = 2.
Then (A) gives f(2) = 4 but f(1) + f(1) = 2. NO!
(B) gives f(2) = 10 and f(1)+f(1) = 10. Maybe let's check the others.
(C) gives f(2) = 5 but f(1) + f(1) = 6. NO!
(D) gives f(2) = \(\sqrt{2}\) while f(1)+f(1) = 2. NO
(E) gives f(2) = 0 and f(1) + f(1) = -2. NO

(B) must be our answer.
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Re: For which of the following functions f(x) is f(a + b) = f(a) ?  [#permalink]

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New post 31 Jul 2018, 17:43
I did not really understand what the question is asking, can someone explain the question?
Thank you in advance
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Re: For which of the following functions f(x) is f(a + b) = f(a) ?  [#permalink]

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New post 01 Aug 2018, 00:50
1
Sandy56 wrote:
I did not really understand what the question is asking, can someone explain the question?
Thank you in advance


I explained very similar question in detail HERE.

Also, check below topics:

13. Functions



For more check below:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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For which of the following functions f(x) is f(a + b) = f(a) ?  [#permalink]

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New post Updated on: 01 Aug 2018, 20:50
2
Sandy56 wrote:
I did not really understand what the question is asking, can someone explain the question?
Thank you in advance


Question asks which of below functions can behave like\(f(a+b)=f(a)+f(b)\).

Now what does\(f(a+b)\) mean ? It can be any function. when we reading question stem we don't know its value. We need to find out of available options.

Now what does\(f(a+b)=f(a)+f(b)\) mean ? it means, for example, f(5)=5 and f(6)=6 then f(5+6)= 5+6= f(5)+(6).

Now check available options one by one.

(A)\(f(x)=x^2\) => \(f(a)=a^2\) , \(f(b)=b^2\) and \(f(a+b)=(a+b)^2\)\(= a^2+2ab+b^2\) which is not equal to \(f(a)+(b)\)

(B)\(f(x)=5x\) =>\(f(a)=5a\), \(f(b)=5b\) and \(f(a+b)=5(a+b)= 5a+5b= f(a) +f(b)\) Whoohoo..here you go. This is the answer :)

(C) \(f(x)=2x+1\)

(D)\(f(x)=\sqrt{x}\)

(E) \(f(x)=x−2\)

Pls find similar question to practice: https://gmatclub.com/forum/for-which-of ... 24491.html

Originally posted by ammuseeru on 01 Aug 2018, 20:38.
Last edited by ammuseeru on 01 Aug 2018, 20:50, edited 1 time in total.
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For which of the following functions f(x) is f(a + b) = f(a) ?  [#permalink]

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New post 01 Aug 2018, 20:41
DavidTutorexamPAL wrote:
Bunuel wrote:
For which of the following functions f(x) is \(f(a + b) = f(a) + f(b)\)?


(A) \(f(x) = x^2\)

(B) \(f(x) = 5x\)

(C) \(f(x) = 2x + 1\)

(D) \(f(x) =\sqrt{x}\)

(E) \(f(x) = x - 2\)


Instead of trying to work with the equations, we'll pick easy numbers to eliminate incorrect answers.
This is an Alternative approach.

Say a = 1 and b = 1, so a+b = 2.
Then (A) gives f(2) = 4 but f(1) + f(1) = 2. NO!
(B) gives f(2) = 10 and f(1)+f(1) = 10. Maybe let's check the others.
(C) gives f(2) = 5 but f(1) + f(1) = 6. NO!
(D) gives f(2) = \(\sqrt{2}\) while f(1)+f(1) = 2. NO
(E) gives f(2) = 0 and f(1) + f(1) = -2. NO

(B) must be our answer.


In my opinion, it is very basic fundamental question. I don't know whether we really need number to put in and check. If student's basic math fundamentals are clear, Student should be able to solve it visually.
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For which of the following functions f(x) is f(a + b) = f(a) ? &nbs [#permalink] 01 Aug 2018, 20:41
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