test

$$ f(x)=\sin ^{-1}\left(\log _{2}\left(\frac{x^{2}}{2}\right)\right) \in \mathbf{R} \Leftrightarrow-1 \leq \log _{2}\left(\frac{x^{2}}{2}\right) \leq 1 \Leftrightarrow \frac{1}{2} \leq \frac{x^{2}}{2} \leq 2 \Leftrightarrow 1 \leq x^{2} \leq 4 \Leftrightarrow x \in[-2,-1] \cup[1,2] $$ 8. The domain of definition of the function, $f(x)$ given by the equation $2^{x}+2^{y}=2$ is (A) $0<\mathrm{x} \leq 1$ (B) $0 \leq \mathrm{x} \leq 1$ (C) $-\infty