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Let f(x) = {x-1)^2 sin(1/(x-1)-|x|,if x...

Let `f(x) = {x-1)^2 sin(1/(x-1)-|x|`,if `x!=1` and -1, if `x=1` 1valued function. Then, the set of pointsf, where `f(x)` is not differentiable, is .... .

Text Solution

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The correct Answer is:
x = 0
Given, `f(x) = {{:((x-1)^(2) sin. 1/((x-1))-|x|", if "x ne 1),(" -1, if " x = 1):}`
As, `f(x) = {{:((x-1)^(2)sin. 1/(x-1) -x", "0le x-{1}),((x-1)^(2)sin 1/((x-1))+x", " x lt 0),(" -1 , " x= 1):}`
Here, f(x) in not differentiable at x = 0 due to |x|.
Thus, f(x) is not differentiable at x = 0 .
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