Calc AP review

[mattflint50]

let f(x)=cosx for x in greater than or equal to zero and less than or equal to 2pi. Let g(x)=ln x for all x is greater than 0. Let S be the composition of g with f; that is S(x)=g(f(x))
A.)find the domain of S
B.)find the range of S
C.)find the zeros of S

Can someone help me get started on this problem.

 

[pka]

By the construction of the problem the domain of f is [0,2pi] therefore the domain of S=gof is a subset of [0,2pi].
Now the domain of ln(x) is the set of positives.
So where is f positive in [0,2pi]?

Once you have that, find the range.