y=sqrt{cosx}+sqrt{25-x^2}
Domain of y=?

Question

y=sqrt{cosx}+sqrt{25-x^2}
Domain of y=?

dls · Answer

I think we need the graph method for this,im confused about that.

anonymous · Answer

Since you can only take the square root of a number $\geq$ 0,
$\cos x \geq 0$ and $25 - x^2 \geq 0$
For the latter one, 
$x^2 \leq 25$, $-5 \leq x \leq 5$

Since we have one root satisfied now we'll look at the other one, taking into account we only have to look on the interval [-5, 5], also note that
$\Large -2\pi < -5 < -\frac{3\pi}{2} \mbox{ and } \frac{3\pi}{2} <  5 < 2\pi$
cos(x) is $\geq$ 0 on $\Large [-{\pi \over 2}, {\pi \over 2}]$ $\Large [\frac{3\pi}{2}, 2\pi]$ and $\Large [-\frac{3\pi}{2}, 2\pi]$

$\Large -5 \leq x \leq -\frac{3\pi}{2} \mbox{ or } -\frac{\pi}{2} \leq x \leq \frac{\pi}{2} \mbox{ or } \frac{3\pi}{2} \leq x \leq 5  $