I presume that h`(x) is the derivative. (I would have used h'(x).)

Use the chain rule:

h'(x)= 2g'(x) f '(2g(x)) and g'(x)= 1/f '(x)

It is easy to calculate that

The only "hard" part, perhaps, is finding g(3). To do that you have to solve so . Fortunately that has an easy soution in [0, 1]!