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Major function help required - GMAT in 2 days

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Senior Manager
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Major function help required - GMAT in 2 days [#permalink] New post 20 Feb 2006, 19:36
Really need your help guys - just dont understand what functions are about at all - simple explanations please.

From GMATPrep:

For which of the following functions f(a+b)=f(a)+f(b) for all positive numbers a and b.

a) f(x) = x^2
b) f(x) = x+1
c) f(x) = sqrtx
d) f(x) = 2/x
e) f(x) = -3x

If any of you guys are feeling particularly generous could you help me understand the geometry problem:

http://www.gmatclub.com/phpbb/viewtopic ... 370#179370
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 [#permalink] New post 20 Feb 2006, 20:00
From an electrical engineering standpoint, a function where f(a+b) = f(a) + f(b) satisfies the principle of "superposition". We EEs were taught to identify such functions by looking for ones with a linear term only (x^2, sqrt x and 1/x need not apply) and no constant term being added (therefore not x + 1). In the list, the only function left is f(x) = -3x.

If you substitute a = b = 1 into the equations as a check, you will see that only e) is valid.
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 [#permalink] New post 21 Feb 2006, 00:36
Easiest way is to calculate f(a+b) and compare with f(a)+f(b)
1. (a+b)^2=a^2+2ab+b^2 <> a^2+b^2
2. a+b+1 <> (a+1)+(b+1)=a+b+2
3. sqr(a+b) <> sqr(a)+sqr(b)
4. 2/(a+b) <> 2/a+2/b=2*(a+b)/ab
5. -3(a+b)=(-3a)+(-3b)
Hence answer is 5.
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 [#permalink] New post 21 Feb 2006, 04:04
Cheers guys, the penny is dropping!
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 [#permalink] New post 21 Feb 2006, 04:19
petefroml wrote:
Easiest way is to calculate f(a+b) and compare with f(a)+f(b)
1. (a+b)^2=a^2+2ab+b^2 <> a^2+b^2
2. a+b+1 <> (a+1)+(b+1)=a+b+2
3. sqr(a+b) <> sqr(a)+sqr(b)
4. 2/(a+b) <> 2/a+2/b=2*(a+b)/ab
5. -3(a+b)=(-3a)+(-3b)
Hence answer is 5.


thnks pete... :)
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vazlkaiye porkalam vazltuthan parkanum.... porkalam maralam porkalthan maruma

  [#permalink] 21 Feb 2006, 04:19
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