Question

Find the functions g and h such that
g(2x)=2g(x).h(x) and
h(2x)=h(x).h(x)-g(x).g(x)

Answer 1

I tried taking (h/g)(x)=y(x), from which we get y(2x)=0.5{y(x)-1/y(x)}. But how to proceed after that?