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.
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.
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.