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Let \mathrm{f(x)=x-|x|}. Then
 

Option: 1

 \mathrm{f(x)} is continuous everywhere
 


Option: 2

 \mathrm{f(x)} is differentiable everywhere

 


Option: 3

 \mathrm{f(x)} is discontinuous at \mathrm{x=0}
 


Option: 4

 \mathrm{f(x)} is not differentiable at \mathrm{x \neq 0}


Answers (1)

best_answer

Both the functions \mathrm{x} and \mathrm{|x|} are continuous everywhere. So, their algebraic sum is also continuous everywhere \mathrm{x} is differentiable everywhere but \mathrm{|x|} is not differentiable at \mathrm{x=0}. So, \mathrm{f(x)} is not differentiable at \mathrm{x=0}.

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Rishabh

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