The intersection of the domains of functions: $\displaystyle f(x) = arcsin(log\frac{x}{10})$ and $\displaystyle g(x) = \sqrt{2+x-x^2}$

a) $\displaystyle [1,2]$

b) $\displaystyle (0,2]$

c) $\displaystyle [1, \infty)$

d) $\displaystyle \phi$

e) $\displaystyle \mathbb{R}_+^*$