# Thread: find the domain of the function

1. ## find the domain of the function

$f(x) = \sqrt{4-x^2}$ + $\sqrt{sinx}$

$\sqrt{4-x^2}$ is defined if $-2 \leq x \leq 2$

$\sqrt{sinx}$ is defined if $2\pi k \leq x \leq \pi + 2 \pi k$

So, to find the domain of the function, am I supposed to determine their union or intersection?

(I think it's the intersection)

$(-2 \leq x \leq 2) \cap (2\pi k \leq x \leq \pi + 2 \pi k) = 0 \leq x \leq 2$

Is that the correct way to find the domain or am I supposed to find their union?

Thanks!

2. Originally Posted by jayshizwiz
$= 0 \leq x \leq 2$
I agree.

3. In order to be able to find a value for f(x), you must be able to calculate both $\sqrt{4- x^2}$ and $\sqrt{sin(x)}$. That is why both " $-2\le x\le 2$" and " $2k\pi\le x\le \pi+ 2k\pi$ must be true.

I think it is amusing that Pickslides says "I agree with you" and just below has his "If I agreed with you we'd both be wrong"!

4. Originally Posted by HallsofIvy
In order to be able to find a value for f(x), you must be able to calculate both $\sqrt{4- x^2}$ and $\sqrt{sin(x)}$. That is why both " $-2\le x\le 2$" and " $2k\pi\le x\le \pi+ 2k\pi$ must be true.

I think it is amusing that Pickslides says "I agree with you" and just below has his "If I agreed with you we'd both be wrong"!
Haha!!