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Question
The domain of the derivative of the function f(x)=⎧⎨⎩tan−1xfor|x|≤112(|x|−1)for|x|>1 is
The domain of the derivative of the function f(x)=⎧⎨⎩tan−1xfor|x|≤112(|x|−1)for|x|>1 is
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Solution
The correct option is C R−{−1}
Given f(x)=⎧⎪
⎪
⎪
⎪
⎪⎨⎪
⎪
⎪
⎪
⎪⎩12(−x−1)if x<−1tan−1xif−1≤x≤112(x−1)if x>1
f(x) is discontinuous at x=−1 and x=1
Therefore domain of f(x)ϵR−{−1,1}
Given f(x)=⎧⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪⎩12(−x−1)if x<−1tan−1xif−1≤x≤112(x−1)if x>1
f(x) is discontinuous at x=−1 and x=1
Therefore domain of f(x)ϵR−{−1,1}
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