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

A function f(x) is defined as follows for real x `f(x)={{:(1-x^(2)","," for "xlt1),(0",","for "x=1),(1+x^(2)","," for "x gt1):},` then

A

f(x) is not continuous at x=1

B

f(x) is continuous but not differentiable at x=1

C

f(x) is both continuous and differentiable at x=1

D

f(x) is continuous everywhere but differentiable no where

Text Solution

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The correct Answer is:
A
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