# Thread: Another composition of functions question

1. ## Another composition of functions question

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].

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

What am I doing wrong? Thanks!

2. Originally Posted by Glitch
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].
$\displaystyle |sin(2x)|$ with domain (-inf, inf)
Note that $\displaystyle 1-\cos^2(x)=\sin^2(x)$, $\displaystyle \sqrt{(x^2)}=|x|$ and $\displaystyle -1\le\sin(x)\le1$.