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I am confused about this problem: Find the domain of the function, $$f(x)=\frac{x^3-1}{2x^2+5}.$$ I'm guessing it's all real numbers but the book gives a different answer.

The book gave $$(-\infty,-1)\cup (-1,0)\cup (0,\infty)$$ as the answer.

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What answer does the book give? It's possible there is a typo. The function you have written down does indeed have all real numbers as its (natural) domain. – Arturo Magidin Jul 14 '11 at 21:46
I have added the book's answer – John1 Jul 14 '11 at 21:53
The answer you write has nothing to do with the function you give. Are you positive you are looking at the right pair question/answer? Maybe that's the answer to a different question? If not, then rest assured that answer is completely, totally, and utterly incorrect. – Arturo Magidin Jul 14 '11 at 21:54
Thanks very much. The online version of the book gave the above answer. So I got a copy of the book itself, and it gave the answer to be $(-\infty, \infty)$. I guess it's just a typo in the online version. – John1 Jul 14 '11 at 22:18
up vote 5 down vote accepted

The book has goofed. You have $2x^2 + 5 \ge 5 > 0$ for all real $x$. Since the denominator has no real zeroes, the function is defined everywhere. Its natural domain in the entire real line.

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