Type 1 Problem for Monday, 9/19

For this problem, refer to the box on page 526.
    Let a>0 be a positive real constant.
  1. Compute the domain of f(x)=sqrt(a^2-x^2).
  2. Compute the range of f(x).
  3. Let the domain of g(t)=a*sin(t) be [-Pi/2,Pi/2]. What is the range of g(t)?
  4. What are the domain and range of the function composition f(g(t))?
  5. If we instead use the substitution x=a*cos(t), so that g(t)=a*cos(t), what is a good choice of domain of g(t) and why?