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Senior | Next Rank: 100 Posts
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by rohanberi » Thu Oct 06, 2011 9:27 pm
For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b ?

f(x) = x^2
f(x) = x + 1
f(x) = sqrt x
f(x) = 2 / x
f(x) = -3x
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by Anurag@Gurome » Thu Oct 06, 2011 9:29 pm
rohanberi wrote:For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b ?

f(x) = x^2
f(x) = x + 1
f(x) = sqrt x
f(x) = 2 / x
f(x) = -3x
This one has been discussed many times on this forum.


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 rohanberi » Fri Oct 07, 2011 1:59 am
Thanks a lot Anurag.

Sorry, didn't check the prior ones.
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