domain of ln{x} where {}is the fractional part

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domain of ln{x} where {}is the fractional part

Asked by farhanaedavath | 22 Jun, 2022, 07:43: PM

Expert Answer

Let f(x) = ln{x}

Now, f(x) is defiined when {x}>0

But space left curly bracket straight x right curly bracket element of left square bracket 0 comma 1 right square bracket space and space left curly bracket straight x right curly bracket equals 0 space when space straight x element of straight Z Therefore comma space domain space of space straight f left parenthesis straight x right parenthesis space is space straight R minus straight Z

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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

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