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by karthikpandian19 » Fri Jan 06, 2012 3:37 pm
For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers of a and b?

f(x) = x^2
f(x) = x+1
f(x) = x^0.5
f(x) = 2/x
f(x) = -3x
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by kp1811 » Fri Jan 06, 2012 4:08 pm
E. f(x) = -3x

f(a+b) = -3(a+b)

f(a) = -3a and f(b) = -3b

so f(a+b) = f(a) + f(b)
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by GMATGuruNY » Fri Jan 06, 2012 4:20 pm
I posted a solution here:

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by Anurag@Gurome » Fri Jan 06, 2012 9:37 pm
karthikpandian19 wrote:For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers of a and b?

f(x) = x^2
f(x) = x+1
f(x) = x^0.5
f(x) = 2/x
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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