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

Question

anonymous · Answer

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

yrivers36 · Answer

anything above -4

anonymous · Answer

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

anonymous · Answer

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

yrivers36 · Answer

so set the bottom equation to 0

anonymous · Answer

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

anonymous · Answer

It just means NOT EQUAL.

yrivers36 · Answer

oh ok

anonymous · Answer

$$5x+3\ne 6 \implies 5x \ne 3 \implies x\ne \frac{5}{3}$$
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 $\pm2$)