The question:

Form the composition fog and give the domain,

$\displaystyle f(x) = \sqrt{1 - x^2}$

$\displaystyle g(x) = cos(2x)$

My attempt:

$\displaystyle (fog)(x) = \sqrt{1 - (cos(2x))^2}$

I worked out the domain of f(x) is [-1, 1], and the domain of g(x) is (-inf, inf). Thus fog must have the domain [-1, 1].

However, the answer is:

$\displaystyle |sin(2x)|$ with domain (-inf, inf)

What am I doing wrong? Thanks!