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If f(x)=cosx+sinx and g(x)=x^(2)-1, then...

If `f(x)=cosx+sinx` and `g(x)=x^(2)-1`, then `g(f(x))` is injective in the interval

A

`[-(pi)/(2),0]`

B

`[-(pi)/(2),pi]`

C

`[-(pi)/(4),(pi)/(4)]`

D

`[0,(pi)/(2)]`

Text Solution

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The correct Answer is:
C
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