Functions

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rohanberi: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Sun Mar 06, 2011 7:42 am; Location: India; Thanked: 2 times

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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Source: Beat The GMAT — Problem Solving | Thu Oct 06, 2011 9:27 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

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)Â² â‰ (aÂ² + bÂ²) => f(a + b) â‰ f(a) + f(b)
2. (a + b + 1) â‰ (a + 1) + (b + 1) = (a + b + 2) => f(a + b) â‰ f(a) + f(b)
3. âˆš(a + b) â‰ (âˆša + âˆšb) => f(a + b) â‰ f(a) + f(b)
4. 2/(a + b) â‰ (2/a) + (2/b) = 2(a + b)/ab => f(a + b) â‰ 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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rohanberi: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Sun Mar 06, 2011 7:42 am; Location: India; Thanked: 2 times

by rohanberi » Fri Oct 07, 2011 1:59 am

Thanks a lot Anurag.

Sorry, didn't check the prior ones.

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