If f(x) is defined on domain [0, 1] then f(2 sin x) is defined on

f(x) is defined on [0,1] ⇒ 0 ≤ x ≤ 1

Now f(2sin x) shall be defined , if $0 ≤ 2 sin x ≤ 1 ⇒ 0 ≤ sin x ≤ \frac{1}{2}$.

 

Hence (A) is the correct answer.