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GMAT Prep - Functions question

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GMAT Prep - Functions question

by tutonaranjo » Fri Aug 24, 2007 4:05 pm
Can someone explain this in detail? No idea how these function questions work.

For which 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) = sqrt x
d) f(x) = 2/x
e) f(x) = -3x

Answer is E
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by mschling52 » Wed Aug 29, 2007 1:37 pm
Best way to go about this one is probably to go through and try out each answer option.

For A,
f(a+b) = (a+b)^2 = a^2 + 2ab + b^2
f(a)+f(b) = a^2 + b^2

so f(a+b) does not equal f(a)+f(b).

For B,
f(a+b) = a + b + 1
f(a)+f(b) = a + 1 + b + 1 = a + b + 2

so f(a+b) not equal f(a)+f(b).

For C,
f(a+b) = sqrt(a+b)
f(a)+f(b) = sqrt(a)+sqrt(b)

so again f(a+b) not equal f(a)+f(b)

For D,
f(a+b) = 2/(a+b)
f(a)+f(b) = 2/a + 2/b

Finally, for E,
f(a+b) = -3(a+b) = -3a - 3b
f(a)+f(b) = -3a + -3b = -3a - 3b
so f(a+b) does equal f(a)+f(b)
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