The function , is
discontinuous at all points.
Differentiable at all points.
Differentiable at all point except at x=1 and x=-1.
Continuous at all points except at x=1 and x=-1, where it is discontinuous.
We have,
So, f(x) is continuous at x=-1.
It can be easily checked that f(x) is also continuous at x=1.
Since f(x) is a polynomial function for and
and a constant function for
. Hence, f(x) is continuous for all x.
We have,
So, f(x) is not differentiable at .
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