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Given x > 0, the values of f(x) = -3cos3+x+x2 lie in the interval ______. - Mathematics

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प्रश्न

Given x > 0, the values of f(x) = `-3cos sqrt(3 + x + x^2)` lie in the interval ______.

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उत्तर

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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अध्याय 3: Trigonometric Functions - Exercise [पृष्ठ ५९]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
अध्याय 3 Trigonometric Functions
Exercise | Q 66 | पृष्ठ ५९

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