Question

Find the domain of the following function:

`f(x)=sin^-1x+sin^-1 2x`

Answer 1

Let f(x) = g(x) + h(x), where g(x)=cotx and h(x)=cot−1x
Therefore, the domain of f(x) is given by the intersection of the domain of g(x) and h(x)
The domain of g(x) is [−1, 1]
The domain of h(x) is `[-1/2, 1/2]`
Therfore, the intersection of g(x) and h(x) is  `[-1/2, 1/2]`
Hence, the domain is `[-1/2, 1/2]`