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Question
Given x > 0, the values of f(x) = `-3cos sqrt(3 + x + x^2)` lie in the interval ______.
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Solution
Given x > 0, the values of f(x) = `-3cos sqrt(3 + x + x^2)` lie in the interval [– 3, 3].
Explanation:
Given that: f(x) = `-3cos sqrt(3 + x + x^2)`
Put `sqrt(3 + x + x^2)` = y
∴ f(x) = –3 cosy
∵ –1 ≤ cosy ≤ 1
3 ≥ –3 cosy ≥ –3
⇒ –3 ≤ –3 cosy ≤ 3
∴ `-3 ≤ -3 cos sqrt(3 + x + x^2) ≤ 3, x > 0`
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