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Let sqrt(((x+1)(x-3))/((x-2))). Find all...

Let `sqrt(((x+1)(x-3))/((x-2)))`. Find all the real values of x for which y takes real values.

Text Solution

Verified by Experts

The correct Answer is:
`x in [-1,2) cup [3,oo)`
Since, `y=sqrt(((x+1)(x-3))/((x-2)))` takes all real values only
when `((x+1)(x-3))/((x-2)) ge 0`

`rArr -1 le x lt 2 or x ge 3`
` therefore x in [-1,2) cup [3,oo)`.
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