Domain of the function f(x) = sin^{-1}left(fr | vedclass

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(C) The function $f(x)$ is defined if the arguments of $\sin^{-1}$,$\cos^{-1}$,and $	an^{-1}$ satisfy their respective domain conditions.For $\sin^{-

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$[-6, 6]$

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(C) The function $f(x)$ is defined if the arguments of $\sin^{-1}$,$\cos^{-1}$,and $	an^{-1}$ satisfy their respective domain conditions.For $\sin^{-1}(u)$ and $\cos^{-1}(u)$,we must have $-1 \leq u \leq 1$.For $	an^{-1}(u)$,$u$ can be any real number.Thus,we require $-1 \leq \frac{2-|x|}{4} \leq 1$.Multiplying by $4$,we get $-4 \leq 2-|x| \leq 4$.Subtracting $2$ from all parts,we get $-6 \leq -|x| \leq 2$.Multiplying by $-1$ (and reversing the inequalities),we get $-2 \leq |x| \leq 6$.Since $|x|$ is always non-negative,the condition $-2 \leq |x|$ is always true for all $x \in R$.Therefore,we only need $|x| \leq 6$,which implies $-6 \leq x \leq 6$.Hence,the domain is $x \in [-6, 6]$.

Domain of the function $f(x) = \sin^{-1}\left(\frac{2-|x|}{4}\right) + \cos^{-1}\left(\frac{2-|x|}{4}\right) + \tan^{-1}\left(\frac{2-|x|}{4}\right)$ is

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