find the domain and the range of the given function f(x)=5/5-x

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find the domain and the range of the given function f(x)=5/5-x

Asked by khanmohammad20510 | 18 Jan, 2022, 10:58: AM

Expert Answer

Given: f(x) = 5/5-x

5 minus straight x space can apostrophe straight t space be space 0 straight i. straight e. space straight x not equal to 5 So comma space the space domain space is space straight R minus open curly brackets 5 close curly brackets Let space straight y equals fraction numerator 5 over denominator 5 minus straight x end fraction rightwards double arrow 5 straight y minus xy equals 5 rightwards double arrow xy equals 5 straight y minus 5 rightwards double arrow straight x equals fraction numerator 5 straight y minus 5 over denominator straight y end fraction Denominator space can apostrophe straight t space be space 0 Therefore space straight y not equal to 0 So comma space the space range space will space be space straight R minus open curly brackets 0 close curly brackets

Answered by Renu Varma | 18 Jan, 2022, 12:59: PM

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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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