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Let f: [-1, 3] → R be defined as
f(x) = { |x| + [x], -1 ≤ x < 1
x + |x|, 1 ≤ x < 2
x + [x], 2 ≤ x ≤ 3
Where [t] denotes the greatest integer less than or equal to t. Then, f is discontinuous at
- four or more points
- only three points
- only two points
- only one point
Correct answer: only two points
Solution
On [-1,1): at x=0 the left limit is -1 but f(0)=0 (jump). At x=1 the left limit is 1 while the next piece gives 2 (jump). At x=2 both sides give 4 (continuous). So f is discontinuous at exactly two points, x=0 and x=1.
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