Another composition of functions question

**Glitch** · July 17th 2010, 05:15 AM

The question:

Form the composition fog and give the domain,

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

My attempt:
$(fog)(x) = \sqrt{1 - (cos(2x))^2}$

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

What am I doing wrong? Thanks!

**Plato** · July 17th 2010, 05:38 AM

Originally Posted by Glitch

The question:

Form the composition fog and give the domain,
$f(x) = \sqrt{1 - x^2}$
$g(x) = cos(2x)$

My attempt:
$(fog)(x) = \sqrt{1 - (cos(2x))^2}$
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:
$|sin(2x)|$ with domain (-inf, inf)