Question
The number of real values of $x$ at which the function $f(x)=\left|\begin{array}{ccc}1 & |x| & x^2 \\1 & |x-1| & (x-1)^2 \\1 & |x-2| & (x-2)^2\end{array}\right|$is not differentiable is
$f(x)=|x-1|(x-2)^2-|x-2|(x-1)^2-|x|$
$\left(( x -2)^2-( x -1)^2\right)+ x ^2(| x -2|-| x -1|)$
$f(x)=|x-1|\left((x-2)^2-x^2\right)+|x-2|\left(x^2-\left(x^2-2 x+1\right)\right)$
$-| x |\left( x ^2-4 x +4- x ^2+2 x -1\right)$
$f ( x )=| x -1|(4-4 x )+| x -2|(2 x -1)-| x |(3-2 x )$
$f(x)=4(1-x)|1-x|+|x-2|(2 x-1)-|x|(3-2 x)$
non-derivable at $x =\frac{1}{2}$ and $x =\frac{3}{2}$
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$g(x)=\left\{\begin{array}{cl}\frac{\sin (x+1)}{(x+1)}, & x \neq-1 \\1, & x=-1\end{array} \text { and } h(x)=2[x]-f(x),\right.$
where $[x]$ is the greatest integer $\leq x$. Then the value of $\lim _{x \rightarrow 1} g(h(x-1))$ is