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For which of the following does f(a)−f(b)=f(a−b)

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For which of the following does f(a)−f(b)=f(a−b)  [#permalink]

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New post 24 Dec 2013, 10:47
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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|

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Re: For which of the following does f(a)−f(b)=f(a−b)  [#permalink]

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New post 24 Dec 2013, 23:26
8
1
madhavsrinivas wrote:
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.


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

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New post Updated on: 28 Feb 2014, 06:26
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 goodyear2013 on 28 Feb 2014, 06:26, edited 1 time in total.
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Re: For which of the following does f(a)−f(b)=f(a−b) for all  [#permalink]

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New post 28 Feb 2014, 00:06
2
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)  [#permalink]

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