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?
First, a remark: a
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
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
. If the equality holds for any a
, we should get an identity, which means the same expression on both sides of the equal sign.
we take the expression of any of the given functions and replace x
. Necessarily ab=0
, which cannot hold, a
being positive. NO
, impossible. NO
NO (check for example a=b=1
NO (again, check for a=b=1
PhD in Applied Mathematics
Love GMAT Quant questions and running.