Question

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

Answer 1

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

Answer 2

anything above -4

Answer 3

\[x^2-4 \ne 0 \implies x^2 \ne 4 \implies x \ne\pm 2\]

Answer 4

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

Answer 5

so set the bottom equation to 0

Answer 6

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

Answer 7

It just means NOT EQUAL.

Answer 8

oh ok

Answer 9

\[5x+3\ne 6 \implies 5x \ne 3 \implies x\ne \frac{5}{3}\]
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 \(\pm2\))