Prove.[Let joint pdf fX.Y(x,y).]X &Y are independent r.v iff fX,Y(x,y)=g(x)h(y).

Question

Prove. Let X &Y be continuous random variables with joint pdf fX,Y(x,y). X and Y are independent iff there exist  functions g(x) and h(y) such that for every x in R and y in R: fX,Y(x,y)=g(x)*h(y)