InterviewSolution
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InterviewSolution
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If x is a real number, then \(\sqrt {log_e\frac{{4x - {x^2}}}{3}} \)is a real number if and only if1. - 3 ≤ x ≤ 32. 1 ≤ x ≤ 23. -1 ≤ x ≤ 34. 1 ≤ x ≤ 3 |
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Answer» Correct Answer - Option 4 : 1 ≤ x ≤ 3 Calculation: According to the question, √(loge(4x – x2)/3) to be a real number, because x is a real number Then, it's root should be greater than 0 ⇒ √(loge(4x – x2)/3) ≥ 0 If, loge = 2.7(Approx) It means logB A ≥ 0 If A ≥ 1 It's true then, B > 1 ⇒ (4x – x2)/3) ≥ 1 ⇒ 4x – x2 ≥ 3 ⇒ x2 – 4x + 3 ≤ 0 ⇒ x2 – 3x – x + 3 ≤ 0 ⇒ (x – 1)(x – 3) ≤ 0 ⇒ x belongs to (1, 3) ∴ x lies between 1 ≤ x ≤ 3. |
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