If f(x+y)=f(x)f(y) and ∑x=1∞f(x)=2,x,y∈N, where N is the set of all natural numbers,  then the value of f(4)f(2) is:

f(x+y)=f(x)·f(y);x,y∈N→(1) and ∑x=1∞f(x)=2→(2) Let f(x)=ax from (2)∑x=1∞ax=2⇒a1-a=2∴a=23∴f(x)=23x  f(4)f(2)=(2/3)4(2/2)2=(2/3)2=4/9