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Q) Find the range of f(x) = x + 1/x Ans) See the image which I have uploaded.. I have just broken the eqn into √x² + 1/√x² +2 -2 ..and have formed the identity (a+b)² and the range is coming  (-∞, 2 ] U [ -2, ∞ ) which is wrong.. the correct range is coming from (a-b)² which is (-∞, -2 ] U [ 2, ∞ ). My Doubt- Why (a+b)² is not giving the correct range? Request- Please send the solution using (a+b)². I've attached an image and let me know if I'm wrong somewhere or why the correct solution isn't coming by using (a+b)². Thanks, Samit  Future Top 50 ranker in JEE ADVANCE
Asked by samithatty | 01 Dec, 2022, 10:32: PM
Expert Answer
For the first case, when x > 0, f(x) can't be negative.
Similarly, for the second case, f(x) can't be positive.
Hence, take the identity (a-b)^2, which gives valid range.
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