Find the domain of `f(x)=2cos^(-1)2x+sin^(-1)x` .

Explanation

To find the domain of the function \( f(x) = 2 \cos^{-1}(2x) + \sin^{-1}(x) \), we need to determine the individual domains of the components \( 2 \cos^{-1}(2x) \) and \( \sin^{-1}(x) \), and then find their intersection.

### Step 1: Determine the domain of \( \sin^{-1}(x) \)

The function \( \sin^{-1}(x) \) is defined for \( x \) in the interval:
\[ -1 \leq x \leq 1 \]
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