yrivers36
  • yrivers36
how do I find the domain of the rational function f(x)= 2/x^2-4?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
What values can x have that won't make the denominator equal 0?
yrivers36
  • yrivers36
anything above -4
anonymous
  • anonymous
\[x^2-4 \ne 0 \implies x^2 \ne 4 \implies x \ne\pm 2\]

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anonymous
  • anonymous
Right? So the domain would be \((-\infty,-2)\;\bigcup\;(-2,2)\;\bigcup\;(2,\infty)\)
yrivers36
  • yrivers36
so set the bottom equation to 0
anonymous
  • anonymous
No, you want to find where it is NOT 0. But you can treat \(\ne\) just like you would \(=\)
anonymous
  • anonymous
It just means NOT EQUAL.
yrivers36
  • yrivers36
oh ok
anonymous
  • 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 \(\pm2\))

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