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The function f(x) = |2sgn(2x)| + 2 has jump discontinuity infinite discontinuity removable discontinuity no discontinuity at x=0

The function f(x) = |2sgn(2x)| + 2 has 
jump discontinuity
infinite discontinuity
removable discontinuity
no discontinuity at x=0

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
f(x) = |2sgn(x)| + 2
Left Hand Limit (LHL):
LHL = \lim_{x\rightarrow 0^{-}} (|2sgn(x)| + 2) = |2.(-1)| + 2 = 4
Right Hand Limit (RHL):
RHL = \lim_{x\rightarrow 0^{+}} (|2sgn(x)| + 2) = |2.(1)| + 2 = 4
f(0) = |2.(0)| + 2 = 2
LHL = RHL\neq f(0)
-> f(x)have finite removable discontinuity at x = 0
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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