The points of discontinuity of the function f defined by $f(x)=\left\{\begin{array}{rc}x+2 & x ≤ 1 \\ x-2 & 1<x<2 \\ 0 & x ≥ 2\end{array}\right.$ are:

1

The correct answer is Option (3) - 1

checking

(i) at x = 1

$f(1)=1+2+3=\lim\limits_{x→1^-}f(x)$

$\lim\limits_{x→1^+}(x-2)=-1$

so $f(1)≠\lim\limits_{x→1^+}(x-2)$ point of discontinuity

(ii) at x = 2

$\lim\limits_{x→2^-}(x-2)=0=f(2)=\lim\limits_{x→2^+}(0)=0$

No discontinuity at x = 1

⇒ only one point of discontinuity