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Consider f(x)=(sqrt(1+x)-sqrt(1-x))/({x}...

Consider `f(x)=(sqrt(1+x)-sqrt(1-x))/({x}) , x!=0 ; g(x)=cos2x , -pi/4 < x < 0 , h(x)=1/sqrt2 f(g(x))` for `x < 0` and `h(x)=1` for `x=0` and `h(x)=f(x)` for `x > 0` then, which of the following holds good (where `{.}` denotes fractional part function) `(A) h` is continuous at `x=0 (B) h` is discontinuous at `x= 0 (C) f(g(x))` is an even function `(D) f(x)` is an even function

A

h' is continous at x=0

B

h' is discontinous at x=0

C

f(g(x)) is an evan function

D

f(x) is an even function

Text Solution

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The correct Answer is:
A
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