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yrivers36

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    What values can x have that won't make the denominator equal 0?

  2. Yrivers36
    • 5 years ago
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    anything above -4

  3. anonymous
    • 5 years ago
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    \[x^2-4 \ne 0 \implies x^2 \ne 4 \implies x \ne\pm 2\]

  4. anonymous
    • 5 years ago
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    Right? So the domain would be \((-\infty,-2)\;\bigcup\;(-2,2)\;\bigcup\;(2,\infty)\)

  5. Yrivers36
    • 5 years ago
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    so set the bottom equation to 0

  6. anonymous
    • 5 years ago
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    No, you want to find where it is NOT 0. But you can treat \(\ne\) just like you would \(=\)

  7. anonymous
    • 5 years ago
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    It just means NOT EQUAL.

  8. Yrivers36
    • 5 years ago
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    oh ok

  9. anonymous
    • 5 years ago
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    \[5x+3\ne 6 \implies 5x \ne 3 \implies x\ne \frac{5}{3}\] 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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