Question

Let f(x) = 1/(x-3) and g(x) = sin2 (x).
(i) Find the domain and range of f.
(ii) Find the domain and range of g.
(iii) Find a formula for (f ◦ g)(x). Hence find (f ◦ g)(1).

Answer 1

(i) all real numbers except where the denominator is zero
(ii) sin and cos have a domain of all real numbers
(f◦g)(x) = f(g(x)) = 1/(sin^2(x) - 3)
so plug in x=1