Continuity,Differentiability

q1 Find intervals of continuity,differentiability

1) sin^-1(1+x²2x)

2) [x[1-x]]
[.] denotes Greatest Integer function

q2 Find Domain and range
1[sinx]

q3 f(x) and g(x) are twice differentaible functions in [0,2].
If f"(x)=g"(x),f'(1)=2,g'(1)=4,f(2)=3,g(3)=9.Find value of f(x)-g(x) at x=4

q4 f:R→R .If \left| f(x)\right| \leq x^2 ,x ε R.Find f'(0)