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The function f(x)=cos^(-1)((2[|sinx|+|co...

The function `f(x)=cos^(-1)((2[|sinx|+|cosx|])/(sin^2x+2sinx+11/4))` is defined if x belongs to (where [.] represents the greatest integer function)

A

`[0,(7pi)/(6)]`

B

`[0,(pi)/(6)]`

C

`[(11pi)/(6)]`

D

`[pi,2pi]`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
`1le|sinx|+|cosx|lesqrt2`
`therefore" "2[|sinx|+|cosx|]=2`
`thereforef(x)` is defined if
`sin^(2)x+2 sin x+(11)/(4)ge2`
`"or "(sinx+1)^(2)ge(1)/(4)`
`"or "sinx+1ge(1)/(2) or sin x+1le-(1)/(2)`
`"or "sinx ge-(1)/(2) or sin le-(3)/(2)` (which is not true)
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Knowledge Check

  • int_(0)^(1)[2x]dx where [] is the greatest integer function :

    A
    1
    B
    `(1)/(4)`
    C
    `(1)/(3)`
    D
    `(1)/(2)`.

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