if f(x)=sinx on 0<(or equal to) to x<(or equal to) 2(pie)

Question

and h(x)=ln x on it's domain, state the domain of h(f(x)

Answer 1

Given domain of f(x)=sin(x) is [0,2π].
The range of f(x) is [-1,1].
Domain of h(x)=log(x) is ]0,&#infin[.
The domain of h(f(x)) is equivalent to that of h(range of f(x))
Since f(0)=0, f(π)=0 and f([π,2π])≤0, they are outside the domain of h(x)=log(x), they must be excluded from the domain of h(f(x)).
Thus the domain of h(f(x)) is
{x ∈ ℝ | ]0,&#960[}

Answer 2

erratum:
Domain of h(x)=log(x) is ]0,&#infin;[.

Answer 3

erratum:
I'll try it again:
Domain of h(x)=log(x) is ]0,∞[.