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GMAT Prep Functions

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GMAT Prep Functions

by gdrea3 » Mon Sep 22, 2008 4:31 am
Which of the following functions is f(a+b)=f(a)+f(b) for all positive numbers for a and b?

A) f(x)=x^2
B) f(x)=x+1
C) f(x)=square root of x
D) f(x)=2/x
E) f(x)=-3x

Answer: E

I have no idea how to approach this problem! Thanks!
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by vivek.kapoor83 » Mon Sep 22, 2008 4:48 am
Solve it like this ;

1.In this option u put, a+b in place of x^2 , which will be (a+b)^2 is not equal to a^2+b^2
...like this 1st place a+b in place of whatever func is given and then put a in that place and b in that func and add it,then see if both a+b and a & b are equal
like in option 5, if u put f(x) = -3x, if u put -3(a+b) = -3a -3b
and if u take RHS,put f(a)= -3a & f(b)= -3b, adding these two , it will be -3a-3b which is equal to f(a+b)
So, answer is E.
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by cramya » Mon Sep 22, 2008 5:15 am
For these type of problems try substituting numbers

Since square root is asked choose perfect squares for a and b(pcik easier numbers too if needed in other situations)

a= 9 b= 16

f(a+b) = f(a) + f(b)
i.e f(25) = f(9) + f(16)

f(25) = -3x = -3*25 = -75
f(9) = -3x = -3*9 = -27
f(16) = -3*16 = -48

f(25) = f(9) + f(16) TRUE

Other choices will evaluate to false and only E will be true
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by cramya » Mon Sep 22, 2008 3:20 pm
I should also add avoid picking 0 or 1 beacuse of the unique propoerties of these 2 numbers when doing certain operatiosn like addition/multiplication

pick other easier numbers too if needed in other situations
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