For all real numbers x and y, if the function y = f (x), satisfies f (XY) = f (x) f (y), and f (0) is not equal to 0, find f (2009) = () Others say: f(0) = f(0)*f(0) => f(0) = 1 f(0) = f(0) * f(2009) = f(2009) = 1 But shouldn't 2009 and 0 satisfy the relation between X and y?

For all real numbers x and y, if the function y = f (x), satisfies f (XY) = f (x) f (y), and f (0) is not equal to 0, find f (2009) = () Others say: f(0) = f(0)*f(0) => f(0) = 1 f(0) = f(0) * f(2009) = f(2009) = 1 But shouldn't 2009 and 0 satisfy the relation between X and y?

f(0) = f(0*2009)=f(0) * f(2009) = f(2009) = 1