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The domain of $f (x) = \cos^{- 1} (\frac{2 - |x|}{4}) + {[\log (3 - x)]}^{- 1}$ is

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-2,6

-6,2∪2,3

-6,2

-2,2∪2,3

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detailed solution

Correct option is B

cos-12-x4 exists if -1≤2-x4≤1or -6≤-x≤2or -2≤x≤6or x≤6or -6≤x≤6The function log3-x-1=1log3-x is defined if 3-x>0 and x≠2 i.e., if x≠2 and x<3.Thus, the domain of the given function is x|-6≤x≤6∩x|x≠2,x<3=-6,2∪2,3

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The domain of fx=cos-12-x4+log3-x-1 is

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The domain of $f (x) = \cos^{- 1} (\frac{2 - |x|}{4}) + {[\log (3 - x)]}^{- 1}$ is