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The function f(x)=(sin(pi[x-pi])) , wher...

The function `f(x)=(sin(pi[x-pi]))` , where `[]` denotes the greatest integer function, is continuous as well as differentiable for all `x in R` (b) continuous for all `x` but not differentiable at some `x` (c) differentiable for all `x` but not continuous at some `x` . (d) none of these

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`f(x)=(sin(pi[x-pi]))`
It is a sine function and we know that sine function is continuous and differentiable everywhere on real line.
Hence,it is continuous and differentiable everywhere on real line.
Thus, option (a) is correct.
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