Let f be a function satisfying f(xy)=f(x)y for all positive real numbers x and y . If f(30)=20 , then the value of f(40) is

An equation of this kind is called a functional equation, and can often be solved by choosing particular values for the variables. In this case, by choosing we see that f(y)=f(1)y for all y. Put y=30;f(1)=30.f(30)=30.20=600. Now f(40)=f(1)40=60040=15