u(x,y)=lnx+lny

v(x,y)=x^2*y^2

v(x,y) is a monotonic function of u(x,y)

v=f(u)

=(1/2)*ln(x^2*y^2)=lnx+lny

how to show that u(x,y) is a monotonic function of v(x,y)

u=g(v)

is that g(v)=e^(2lnx+2lny)?