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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.

Fytch
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ramin
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    For future reference, you can use MathJax to render maths on this site. Here is a quick tutorial – praeseo Jul 19 '18 at 09:31
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    The symbol of floor is $\lfloor:\rfloor$. See : https://tex.stackexchange.com/questions/118173/how-to-write-ceil-and-floor-in-latex – JJacquelin Jul 19 '18 at 09:34

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

Mostafa Ayaz
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