Consider the following statements in respect of f(x)=|x|-1 : 1. f(x) is continuous at x=1 . 2. f(x) is differentiable at x=0 . Which of the above statements is/are correct?

Step-by-step solution

Here, f(x)=|x|-1 f(x) array cc -x-1, & x 0 x-1, & x 0 array . For continuity at x=1 . aligned & LHL = _ x 1⁻ f(x)= _ x 1⁻ (x-1)=1-1=0 & RHL = _ x 1⁺ f(x)= _ x 1⁺ (x-1)=1-1=0 aligned f(x) is continuous at x=1 . For differentiability at x=0 . aligned & f^ (x)= array cc -1, & x 0 1, & x 0 array . & LHD = _ x 0⁻ f^ (x)= _ x 0⁻ (-1)=-1 & RHD = _ x 0⁺ f^ (x)= _ x 0⁺ (1)=1 aligned f(x) is not differentiable at x=0