I frequently have trouble trying to place limits on Solve or Reduce using assumptions and domains. For example, this code:
Assuming[x > 0 && x < 1, Solve[(1 - (1 - x)^3)^3 == x, x, Reals]]
Produces results both with complex number, and with x outside the range specified. The exact output is long (and includes the desired results), but a subset is pasted below. What is going on? $\left\{\{x\to 0\},\{x\to 1\},\left\{x\to 1-\frac{\left(1-i \sqrt{3}\right) \left(\frac{1}{2} \left(-9+\sqrt{93}\right)\right)^{1/3}}{2 3^{2/3}}+\frac{1+i \sqrt{3}}{2^{2/3} \left(3 \left(-9+\sqrt{93}\right)\right)^{1/3}}\right\}\right\}$