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# For which of the following does f(a)−f(b)=f(a−b) for all values of a

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Intern
Joined: 30 Nov 2013
Posts: 17
Location: India
Concentration: Finance, General Management
GMAT 1: 640 Q50 V25
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WE: Information Technology (Computer Software)
For which of the following does f(a)−f(b)=f(a−b) for all values of a  [#permalink]

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24 Dec 2013, 10:47
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63% (01:29) correct 37% (01:38) wrong based on 289 sessions

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For which of the following does f(a)−f(b)=f(a−b) for all values of a and b?

A) f(x)=x^2
B) f(x)=x/2
C) f(x)=x+5
D) f(x)=2x−1
E) f(x)=|x|
Manager
Joined: 19 Apr 2013
Posts: 66
Concentration: Entrepreneurship, Finance
GMAT Date: 06-05-2015
GPA: 3.88
WE: Programming (Computer Software)
Re: For which of the following does f(a)−f(b)=f(a−b) for all values of a  [#permalink]

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24 Dec 2013, 23:26
12
1
1
For which of the following does f(a)−f(b)=f(a−b) for all values of a and b?

A) f(x)=x^2
B) f(x)=x/2
C) f(x)=x+5
D) f(x)=2x−1
E) f(x)=|x|

Hi,

To solve this easiest way is just put the value and see that if it equals or not.

with option 1. f(a) = a^2 and f(b) = b^2

so L.H.S = a^2 - b^2

and R.H.S = (a-b)^2 ==> a^2 + b^2 -2ab.

so L.H.S not equal to R.H.S

with option 2. f(a) = a/2 and f(b) = b/2

L.H.S = a/2 - b/2 ==> 1/2(a-b)

R.H.S = (a-b)/2

so L.H.S = R.H.S which is the correct answer.

you can try simile for other option.

Thanks,
AB

+1 Kudos if you like and understand.

##### General Discussion
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Joined: 02 Sep 2009
Posts: 65762
Re: For which of the following does f(a)−f(b)=f(a−b) for all values of a  [#permalink]

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28 Feb 2014, 00:06
3
1
goodyear2013 wrote:
For which of the following does f(a)−f(b)=f(a−b) for all values of a and b?
f(x)=x^2
f(x)=x/2
f(x)=x+5
f(x)=2x−1
f(x)=|x|

OE
Since, via the distributive property, x(a + b) = ax + bx, you can safely say that any division or multiplication will not change the value of f(a - b) equalling f(a) - f(b). For any of the others, however, there exist many values for which there will be different results.

Hi, I want to know how we can approach this question, please.

Merging similar topics. Please refer to the solution above and ask if anything is unclear.

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Hope this helps.
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Re: For which of the following does f(a)−f(b)=f(a−b) for all values of a  [#permalink]

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14 May 2019, 13:13
2
For which of the following does f(a)−f(b)=f(a−b) for all values of a and b?

A) f(x)=x^2
B) f(x)=x/2
C) f(x)=x+5
D) f(x)=2x−1
E) f(x)=|x|

Another way to look to this question

let a=3 & b=2

Question becomes : For which of the following functions does f(3) - f(2) = f(1)?

f(3) = 9
f(2) = 4
f(1) = 1
9 - 4=5........Eliminate

f(3) = 3/2
f(2) = 1
f(1) = 1/2
3/2 - 1= 1/2........Keep

f(3) = 8
f(2) = 7
f(1) = 6
8 - 7= 1........Eliminate

f(3) = 5
f(2) = 3
f(1) = 1
5 - 3= 2........Eliminate

f(3) = 3
f(2) = 2
f(1) = 1
3 - 2= 1........Keep

So we can choose another example. Let a=2 & b=3

f(2) = 2
f(3) = 3
f(1) = 1
2 - 3= -1.......Eliminate

only one answer fits

Senior Manager
Joined: 21 Oct 2013
Posts: 407
For which of the following does f(a)−f(b)=f(a−b) for all values of a  [#permalink]

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Updated on: 14 May 2019, 20:29
1
For which of the following does f(a)−f(b)=f(a−b) for all values of a and b?
f(x)=x^2
f(x)=x/2
f(x)=x+5
f(x)=2x−1
f(x)=|x|

OE

Since, via the distributive property, x(a + b) = ax + bx, you can safely say that any division or multiplication will not change the value of f(a - b) equalling f(a) - f(b). For any of the others, however, there exist many values for which there will be different results.

Originally posted by goodyear2013 on 27 Feb 2014, 11:00.
Last edited by Bunuel on 14 May 2019, 20:29, edited 2 times in total.
Senior Manager
Joined: 10 Jan 2013
Posts: 307
Location: India
Concentration: General Management, Strategy
GPA: 3.95
Re: For which of the following does f(a)−f(b)=f(a−b) for all values of a  [#permalink]

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14 May 2019, 20:28
For which of the following does f(a)−f(b)=f(a−b) for all values of a and b?
A) f(x)=x^2
B) f(x)=x/2
C) f(x)=x+5
D) f(x)=2x−1
E) f(x)=|x|

My approach:
one can be easily confused in this type of question.. so please proceed slowly.

1. f(x)= x^2
LHS --> a^2 - b^2
RHS --> (a-b)^2

LHS != RHS ---> Reject

2. f(x) = x/2
LHS --> (a/2) - (b/2)
RHS --> (a-b)/2

LHS = RHS

No need to check further
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Posts: 15592
Re: For which of the following does f(a)−f(b)=f(a−b) for all values of a  [#permalink]

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29 May 2020, 09:09
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Re: For which of the following does f(a)−f(b)=f(a−b) for all values of a   [#permalink] 29 May 2020, 09:09

# For which of the following does f(a)−f(b)=f(a−b) for all values of a

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