The value of ๐‘ for which the function ๐‘“(๐‘ฅ) = ๐‘ฅ + ๐‘๐‘œ๐‘  ๐‘ฅ + ๐‘ is strictly decreasing over R is:

(a) ๐‘ < 1  (b) No value of b exists

(c) ๐‘ ≤ 1  (d) ๐‘ ≥ 1

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  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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Question 29 The value of ๐‘ for which the function ๐‘“(๐‘ฅ) = ๐‘ฅ + ๐‘๐‘œ๐‘  ๐‘ฅ + ๐‘ is strictly decreasing over R is: (a) ๐‘ < 1 (b) No value of b exists (c) ๐‘ โ‰ค 1 (d) ๐‘ โ‰ฅ 1 Given ๐‘“(๐‘ฅ) = ๐‘ฅ + ๐‘๐‘œ๐‘  ๐‘ฅ + ๐‘ Now, ๐‘“โ€™(๐‘ฅ) = 1 โˆ’ sin x Since ๐‘“(๐‘ฅ) is strictly decreasing over R ๐‘“โ€™(๐‘ฅ) < 0 1 โˆ’ sin x < 0 1 < sin x sin x > 1 Since โˆ’1 โ‰ค sin x โ‰ค 1 Thus, sin x > 1 is not possible Thus, for no value of b, ๐‘“(๐‘ฅ) is strictly decreasing So, the correct answer is (B)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.