Plug in a=2 and b=3. Thus, a+b=5. The question becomes:vishalrb wrote:Source: GMATPrep
For which of the following functions is f(a+b) =f(a) + f(b) for all positive integers a and b?
a. f(x) = x^2
b. f(x) = x + 1
c. f(x) = x^1/2
d. f(x) = 2/x
e. f(x) = -3x
For which of the following functions does f(5) = f(2) + f(3)?
Answer choice A:
f(5) = 5^2 = 25.
f(2) = 2^2 = 4.
f(3) = 3^2 = 9.
25 = 4+9.
Doesn't work. Eliminate A.
Answer choice B:
f(5) = 5+1 = 6.
f(2) = 2+1 = 3.
f(3) = 3+1 = 4.
6 = 3+4.
Doesn't work. Eliminate B.
Answer choice C:
f(5) = √5
f(2) = √2
f(3) = √3
√5 = √2+√3.
Doesn't work. Eliminate C.
Answer choice D:
f(5) = 2/5.
f(2) = 2/2 = 1.
f(3) = 2/3.
2/5 = 1 + 2/3.
Doesn't work. Eliminate D.
The correct answer is E.
Answer choice E:
f(5) = -3*5 = -15.
f(2) = -3*2 = -6.
f(3) = -3*3 = -9.
-15 = -6 + -9.
Success!
