4
$\begingroup$

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.

$\endgroup$
4
  • 3
    $\begingroup$ 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. $\endgroup$ – Arturo Magidin Jul 14 '11 at 21:46
  • $\begingroup$ I have added the book's answer $\endgroup$ – John1 Jul 14 '11 at 21:53
  • 6
    $\begingroup$ 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. $\endgroup$ – Arturo Magidin Jul 14 '11 at 21:54
  • $\begingroup$ 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. $\endgroup$ – John1 Jul 14 '11 at 22:18
5
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.