Let f : [–1, 3] → R be defined as f(x) = ,where [t] denotes the greatest integer less than or equal to t. Then f, is discontinuous at

Engineering

Mathematics

Basic Definition of Continuity

Piecewise Defined Functions

Question

Let f : [–1, 3] → R be defined as f(x) = ${\begin{cases} | x | + [x], - 1 \leq x < 1 \\ x + | x |, 1 \leq x < 2 \\ x + [x], 2 \leq x \leq 3 \end{cases}$ ,

where [t] denotes the greatest integer less than or equal to t. Then f, is discontinuous at

only two points

only three points

only one point

four or more points

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$f (x) = {\begin{cases} - x - 1; x \in [- 1, 0] \\ x; x \in [0, 1] \\ 2 x; x \in [1, 2] \\ x + 2; x \in [2, 3) \\ 6; x = 3 \end{cases}$

f (x) is discontinuous at x = 0, 1,3