The function f(x)=|x-3|, x ∈ R is:

The correct answer is Option (4) → differentiable for all $x \in R$, except x = 3

$f(x)=|x-3|$ so $f(x)=\left\{\begin{matrix}x-3&x≥3\\3-x&x<3\end{matrix}\right.$

$f'(x)=\left\{\begin{matrix}1&x≥3\\-1&x<3\end{matrix}\right.$

at $x=3$ 

LHD ≠ RHD

otherwise differentiable