finding g if f ○ g = F?

Question

If f = (x-1)/x and F = 1 - (1/√x)

what does g equal if f ○ g = F

also for f = sin(2x) and F = sin(x²)

Answer 1

f(g(x))=F
(g(x)-1)/g(x)=1-(1/√x)
1-1/g(x)=1-(1/√x)
1/g(x)=1/√x
g(x)=√x

f(g(x))=F
sin(2g(x))=sin(x^2)
2g(x)=x^2
g(x)= x²/2