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The range of the function f(x)=cos^(2)x ...

The range of the function `f(x)=cos^(2)x -5 cosx -9` is :

A

`[-13, 3]`

B

`[0, 3]`

C

`[-13,-3]`

D

`[-13,-9]`

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x) =cos^(2)x -5 cosx -9`
`= (cos^(2)x -5 cos x +(25)/(4)) -9-(25)/(4)`
`=(cosx -(5)/(2))^(2) -(61)/(4) " " ….(i)`
where `(9)/(4) le (cosx -(5)/(2))^(2) le (49)/(4) " " …(ii)`
`:.` from (i) and (ii) `-13 le f(x) le -3`
`rArr` Range of `f(x) in [-13-3]`
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