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A function f is defined as follows f(x)...

A function f is defined as follows
`f(x)={(1, "when"-inftyltxlt0),(1+sinx, "when 0"lexlepi/2),(2+(x-pi/2)^2, "when" pi/2lexlt infty):}`

A

f(x) is continuous at `x=pi/2`

B

f(x) is continuous at x=0

C

f(x) is discontinuous at x=0

D

f(x) is continuous over the whole real number

Text Solution

Verified by Experts

The correct Answer is:
D
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