find the domain of this function ( [ ] is symbol of floor)

Question

Find the domain of the function $f(x)=\frac{\log(3x-2x^2)}{\left \lfloor 2x-1 \right \rfloor^2 - 1}$ where $\lfloor \cdot \rfloor$ is the floor function.

Answer 1

The domain is$$D=\{x\in\Bbb R\quad,\quad 3x-2x^2>0,[(2x-1)^2]\ne1\}=\{x\in\Bbb R\quad,\quad 0<x<\dfrac{3}{2},[(2x-1)^2]\ne1\}=(0,1)\cup[\dfrac{1+\sqrt 2}{2},\dfrac{3}{2})$$