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Consider the piecewise defined function ...

Consider the piecewise defined function `f(x) = {{:(sqrt(-x),"if",x lt 0),(0,"if",0 le x le 4),(x - 4,"if",x gt 4):}` choose the answer which best describes the continuity of this function.

A

the function is unbounded and therefore cannot be continuous

B

the function is right continuous at x = 0

C

the function has a removable discontinuity at 0 and 4, but is continuous on the rest of the real line.

D

the function is continuous on the entire real line

Text Solution

Verified by Experts

The correct Answer is:
D
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