Let f ( x ) = { | 1 - 2 x 2 | , 0 x 1 | x 2 - 2 x | , 1 x 2 If m , n are number of points of discontinuity and non-differentiability

Question

Let $f (x) =$ ${\begin{matrix} | 1 - 2 x^{2} |, & 0 \leq x < 1 \\ | x^{2} - 2 x |, & 1 \leq x < 2 \end{matrix}$

If $m, n$ are number of points of discontinuity and non-differentiability of $f (x)$ in (0, 2) then ( $[\cdot]$ represents greatest integer function)

Smart Achievers · Accepted Answer

(1)

$By the graph of y = f (x) clearly, f (x) is discontinuous at x = 1$ $and f (x) is non-differentiable at$ $x = \frac{1}{\sqrt{2}} and x = 1$

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