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The function \mathrm{f(x)=\max \{(1-x),(1+x), 2\}} is where \mathrm{x \in(-\infty, \infty)}

Option: 1

discontinuous at all points


Option: 2

differentiable at all points


Option: 3

differentiable at all points except -1 and 1


Option: 4

 continuous at all points except -1 and 1


Answers (1)

We draw the graph of \mathrm{y=1-x, y=1+x\: and \: y=2}
\mathrm{f(x)=\max .\{1-x, 1+x, 2\}}



\mathrm{\therefore \quad f(x)=\left\{\begin{array}{cc} 1-x, \quad x \leq-1 \\ 2, \quad-1<x<1 \\ 1+x, \quad x \geq 1 \end{array}\right.}

From graph it is clear that \mathrm{f\left ( x \right )} is continuous at all \mathrm{x}  and differentiable at all \mathrm{x} except \mathrm{x=-1} and \mathrm{x=1} 

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Kshitij

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