## anonymous 5 years ago how do I find the domain of the rational function f(x)= 2/x^2-4?

1. anonymous

What values can x have that won't make the denominator equal 0?

2. anonymous

anything above -4

3. anonymous

$x^2-4 \ne 0 \implies x^2 \ne 4 \implies x \ne\pm 2$

4. anonymous

Right? So the domain would be $$(-\infty,-2)\;\bigcup\;(-2,2)\;\bigcup\;(2,\infty)$$

5. anonymous

so set the bottom equation to 0

6. anonymous

No, you want to find where it is NOT 0. But you can treat $$\ne$$ just like you would $$=$$

7. anonymous

It just means NOT EQUAL.

8. anonymous

oh ok

9. anonymous

$5x+3\ne 6 \implies 5x \ne 3 \implies x\ne \frac{5}{3}$ So if we are given that 5x+3 is not 6, the only thing we can know for sure is that x is not 5/3. We don't know what it equals (and in your case it can equal anything except $$\pm2$$)