What is the inverse function of $\ x^2+x$? I think the title says it all; I'm looking for the inverse function of $\ x^2+x$, and I have no idea how to do it. I thought maybe you could use the quadratic equation or something. I would be interesting to know.

We  can write $x^2+x=(x+\frac{1}{2})^2 - \frac{1}{4}$ by completing the square. If you restricted yourself to the domain $x \ge -\frac{1}{2}$ then this function would be invertible, and its inverse would be the function
$$x \mapsto \sqrt{x+\frac{1}{4}} - \frac{1}{2}$$
You could do a similar thing on the domain $x \le -\frac{1}{2}$; but the function has no well-defined inverse on $\mathbb{R}$.
