1.
The domain of the function
f(x)=sin⁡−1[2x2−3]+log⁡2(log⁡12(x2−5x+5))f(x)=\sin^{-1}\left[2x^2-3\right]+\log_2\left(\log_{\frac12}\left(x^2-5x+5\right)\right)
, where [t][t] is the greatest integer function, is: