functions f(a + b) = f(a) + f(b) for all positive numbers...

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galinaphillips: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Sat May 26, 2007 10:12 am; Thanked: 1 times

functions f(a + b) = f(a) + f(b) for all positive numbers...

by galinaphillips » Sat Jun 02, 2007 4:44 am

My question is how to solve this problem from the MBA.com software test 1:

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

Possible answers are:

f(x) = x^2

f(x) = x + 1

f(x) = sqrt x

f(x) = 2/x

f(x) = -3x

The correct answer is f(x) = -3x but I'm not sure how to solve.

Thanks!

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Source: Beat The GMAT — Problem Solving | Sat Jun 02, 2007 4:44 am

mschling52: Master | Next Rank: 500 Posts; Posts: 105; Joined: Mon Sep 18, 2006 12:34 pm; Location: OH; Thanked: 7 times; GMAT Score:780

by mschling52 » Sat Jun 02, 2007 12:02 pm

The approach I would take is to plug in a+b in place of x into each function (this is f(a+b)) then see if you can rearrange to get something equal to f(a)+f(b).

A. f(a+b) = (a+b)^2 = a^2 + 2ab + b^2 = f(a)+f(b)+2ab
B. f(a+b) = a + b + 1 = f(b) + a
C. f(a+b) = sqrt(a+b) not equal f(a)+f(b) = sqrt(a)+sqrt(b)
D. f(a+b) = 2/(a+b) not equal f(a)+f(b) = 2/a + 2/b
E. f(a+b) = -3(a+b) = -3a+-3b = f(a)+f(b)