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anonymous
 5 years ago
how do I find the domain of the rational function f(x)= 2/x^24?
anonymous
 5 years ago
how do I find the domain of the rational function f(x)= 2/x^24?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0What values can x have that won't make the denominator equal 0?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[x^24 \ne 0 \implies x^2 \ne 4 \implies x \ne\pm 2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Right? So the domain would be \((\infty,2)\;\bigcup\;(2,2)\;\bigcup\;(2,\infty)\)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so set the bottom equation to 0

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No, you want to find where it is NOT 0. But you can treat \(\ne\) just like you would \(=\)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It just means NOT EQUAL.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[5x+3\ne 6 \implies 5x \ne 3 \implies x\ne \frac{5}{3}\] 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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