BigUp wrote:

Hello GmatClub,

Could someone please help me to understand this gmatprep question? Thanks!

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

First, a remark:

a and

b are considered positive because the function in C, the square root is not defined for negative numbers and the function in D is not defined for

x=0 (

x being in the denominator). The other functions are defined for any real number.

For each function, we translate the given equality and check whether is holds for any positive

a and

b. If the equality holds for any

a and

b, we should get an identity, which means the same expression on both sides of the equal sign.

For

f(a+b) we take the expression of any of the given functions and replace

x by

(a+b).

(A)

(a+b)^2=a^2+b^2 or

a^2+2ab+b^2=a^2+b^2. Necessarily

ab=0, which cannot hold,

a an

b being positive. NO

(B)

a+b+1=a+1+b+1 gives

1=2, impossible. NO

(C)

\sqrt{a+b}=\sqrt{a}+\sqrt{b} NO (check for example

a=b=1)

(D)

\frac{2}{a+b}=\frac{2}{b}+\frac{2}{b} NO (again, check for

a=b=1)

(E)

-3(a+b)=-3a+(-3b) or

-3a-3b=-3a-3b YES!!!

Answer E.

_________________

PhD in Applied Mathematics

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