$f(x) = \left\{ {\begin{array}{*{20}{r}}{1 + x;}&{x > 1}\\{2;}&{ - 1 \le x \le 1}\\{1 - x;}&{x < - 1}\end{array}} \right.$
Since $f(x) = 1 - x$ or $1 + x$ are polynomial functions and $f(x) = 2$ is a constant function.
$\therefore$ These are continuous at all points.....$(i)$
$\therefore$ $f(x)$ is differentiable at all the points, except at
$x = 1$ and at $x = - 1$.....$(ii)$
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Statement $-2$ : $f(x) = \frac{1}{{\sqrt {1 - {x^2}} }} + \left[ {\frac{{{x^2} + x + 1}}{4}} \right]$ , where $[.]$ is greatest integer function. Function $f(x)$ is even function