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The range of function f(x)=cos^2x -5 cos...

The range of function `f(x)=cos^2x -5 cos x -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 cos x -9`
`=(cos^(2)x -5 cos x +(25)/(4)) -9-(25)/(4)`
`=(cos x -(5)/(2))^(2) -(61)/(4)" "…(i)`
where `(9)/(4) le (cos x -(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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