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problem with functions Gmat Prep

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by nimish » Mon Sep 26, 2011 6:07 pm
IMO - e
f(x)=-3x
so, f(a+b) = -3(a+b)=-3a-3b
f(a)+f(b)= -3a+(-3b)=-3a-3b
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by Anurag@Gurome » Mon Sep 26, 2011 6:10 pm
Taniuca wrote:For wich of the following functions is 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) = SQRx
d)f(x)= 2/x
e)f(x)=-3x

Let's analyze each of the options individually:

1. (a + b)² ≠ (a² + b²) => f(a + b) ≠ f(a) + f(b)
2. (a + b + 1) ≠ (a + 1) + (b + 1) = (a + b + 2) => f(a + b) ≠ f(a) + f(b)
3. √(a + b) ≠ (√a + √b) => f(a + b) ≠ f(a) + f(b)
4. 2/(a + b) ≠ (2/a) + (2/b) = 2(a + b)/ab => f(a + b) ≠ f(a) + f(b)
5. (-3(a + b)) = (-3a) + (-3b) => f(a + b) = f(a) + f(b)

The correct answer is E.
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by GMATGuruNY » Mon Sep 26, 2011 7:35 pm
I posted an alternate solution here:

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