If f(x)=|1−x|, then the points where sin−1(f|x|) is non-differentiable are
A
{0,1}
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B
{0,−1}
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C
{0,1,−1}
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D
None of these
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Solution
The correct option is C{0,1,−1} Given that f(x)=|1−x| ⇒f(|x|)=⎧⎪
⎪
⎪⎨⎪
⎪
⎪⎩x−1x>11−x0<x≤11+x−1≤x≤0−x−1x<−1 Clearly the domain of sin−1(f|x|)is[−1,1]. ⇒ It is non differentiable at the points {−1,0,1}