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Which of the following functions is/are ...

Which of the following functions is/are not discontinuous at `x=1?`

A

`f(x)=(1)/(1+2^(tanx))`

B

`g(x)=underset(n rarroo)(lim)(1)/(1+n sin^(2)(pix))`

C

`h(x)=2^(-2^(((1)/(1-X)))),x ne 1 andh(1)=1`

D

`phi(x)=(x-1)/(|x-1|+2(x-1)^(2)),x ne 1 and phi(1)=1`

Text Solution

Verified by Experts

The correct Answer is:
A
(a) Clearly, f(x) is continuous at x = 1.
(b) `g(1^(+))=0,g(1)=1rArrg(x)` is discontinuous at x = 1
(c) `h(1^(+))=1 and h(1^(-))=0rArr h(x)` is discontinuous at x = 1
(d) `phi(1^(+))=1 and phi(1^(-))=-1rArr phi(x)` is discontinuous at x = 1
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