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Let f:[-pi/3,(2pi)/3] rarr [0,4] be a fu...

Let `f:[-pi/3,(2pi)/3] rarr [0,4]` be a function defined as `f(x)=sqrt(3)sinx-cosx+2.` Then `f^(-1)(x)` is given by
`(a)` `sin^(-1)((x-2)/2)-pi/6`
`(b)` `sin^(-1)((x-2)/2)+pi/6`
`(c)` `(2pi)/3+cos^(-1)((x-2)/2)`
`(d)` none of these

A

`f ^(-1) (1) =(4pi)/(3)`

B

`f ^(-1) (1)=pi`

C

`f ^(-1) (2) =(5pi)/(6)`

D

`f ^(-1) (2) =(7pi)/(6)`

Text Solution

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The correct Answer is:
A, D
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