The points of discontinuity of the function f defined by \(f(x)=\begin{cases} x+2 & x \le 1 \\ x-2 & 1 \lt x \lt 2 \\ 0 & x \ge 2 \end{cases}\) are:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1
Each piece is a polynomial, so f is continuous at every point except possibly where the definition changes, x = 1 and x = 2. Check the left-hand and right-hand limits there.
At x = 1:
\(\text{LHL} = 1 + 2 = 3 = f(1)\)
\(\text{RHL} = 1 - 2 = -1\)
The limits differ, so f is discontinuous at x = 1.
At x = 2:
\(\text{LHL} = 2 - 2 = 0\)
\(\text{RHL} = 0,\quad f(2) = 0\)
All three are equal, so f is continuous at x = 2.
Hence the only point of discontinuity is x = 1.