Find the domain of the following function:f(x)= ^ -1 x+ ^ -1 2x - Vidyadip

Question

Find the domain of the following function:$\text{f(x)}=\sin^{-1}\text{x}+\sin^{-1}2\text{x}$

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Answer

Let f(x) = g(x) + h(x), where
Therefore the domain of f(x) is given by intersection of the domain of g(x) and h(x)
The domain of g(x) is [-1, 1]
The domain of h(x) is $\Big[-\frac{1}{2},\frac{1}{2}\Big]$
Therefore, the intersection of g(x) and h(x) is $\Big[-\frac{1}{2},\frac{1}{2}\Big]$
Hence, the domain is $\Big[-\frac{1}{2},\frac{1}{2}\Big]$

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