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  • The interval of x for the inequality  <img alt="\\\mathrm{\frac{x}{x-1} \geq 0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5C%5C%5Cmathrm%7B%5Cfrac%7Bx%7D%7Bx-1%7D%20%5Cgeq%20

The interval of x for the inequality  \\\mathrm{\frac{x}{x-1} \geq 0}  is

Option: 1

\mathrm{x\in(0,1]}


Option: 2

\mathrm{x\in[0,1)}


Option: 3

\mathrm{x\in(-\infty,0]\cup (1,\infty)}


Option: 4

\mathrm{x\in(-\infty,0)\cup [1,\infty)}


Answers (1)

best_answer

Here, critical points are x=0,1

 

The critical points are marked on the real number line. Starting with a positive sign in the rightmost interval, we denote signs of adjacent intervals by the alternating sign.

Hence, \mathrm{x\in(-\infty,0]\cup (1,\infty)}

 

correct option is (c)

Posted by

Deependra Verma

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