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If $f(x)=\left\{\begin{matrix}[\cos πx],&x<1\\|x-2|,&1≤x<2\end{matrix}\right.$ ([*] denotes the greatest integer function), then f(x) is |
continuous and non-differentiable at x = –1 and x = 1 continuous and differentiable at x = 0 discontinuous at x = 1/2 continuous but not differentiable at x = 2 |
discontinuous at x = 1/2 |
We have, $f(x)=\left\{\begin{matrix}[\cos πx],&x<1\\|x-2|,&1≤x<2\end{matrix}\right.$ $= 2 – x, 1≤x<2\left\{\begin{matrix}-1,&\frac{1}{2}<x<1\\0,&0<x≤\frac{1}{2}\\0,&-\frac{1}{2}≤x<0\\-1,&-\frac{3}{2}<x<-\frac{1}{2}\end{matrix}\right.$ It is evident from the definition that f(x) is discontinuous at x = 1/2. |
