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Question 20 Statement A Assertion (A): The function 𝑓:𝑅−{(2𝑛+1)𝜋/2:𝑛∈𝑍}→(−∞,−1]∪[1,∞) defined by 𝑓(𝑥)=sec 𝑥 is not one-one function in its domain. Statement R Reason (R): The line 𝑦=2 meets the graph of the function at more than one point. (A) Both (A) and (R) are true and (R) is the correct explanation of (A). (B) Both (A) and ( 𝑅 ) are true but (𝑅) is not the correct explanation of (𝐴). (C) (A) is true but (R) is false. (D) (A) is false but (𝑅) is true.Checking Assertion Assertion (A): The function 𝑓:𝑅−{(2𝑛+1)𝜋/2:𝑛∈𝑍}→(−∞,−1]∪[1,∞) defined by 𝑓(𝑥)=sec 𝑥 is not one-one function in its domain. Given 𝑓(𝑥)=sec⁡𝑥 Now, sec⁡〖𝜋/3〗=2 sec⁡〖(−𝜋)/3〗=2 Also, sec⁡〖5𝜋/3〗=2 sec⁡〖(−5𝜋)/3〗=2 Since sec x = 2 is for more than one value of x ∴ 𝑓(𝑥)=sec⁡𝑥 is not a one-one function ∴ Assertion is true Checking Reason Reason (R): The line 𝑦=2 meets the graph of the function at more than one point. Since 𝑓(𝑥)=sec 𝑥 Thus, 𝑦=2 means 𝐬𝐞𝐜 𝒙=𝟐 And sec x = 2 is true for x = 𝝅/𝟑,(−𝝅)/𝟑,𝟓𝝅/𝟑,(−𝟓𝝅)/𝟑… So, line 𝑦=2 meets the graph of f(x) at more than one point ∴ Reasoning is true Is Reason a Correct explanation for Assertion? Since sec x = 2 is for more than one value of x And, it means that line 𝑦=2 meets the graph of f(x) at more than one point Therefore, Reasoning is a correct explanation for Assertion So, Assertion is true Reasoning is true And, Reasoning is a correct explanation for Assertion So, the correct answer is (a)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.