How do you find the domain and range of $p(x) = sqrt{3/(x - 2)}$ ?

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Answer 1 · 2017-11-04T15:06:48

Domain is $x>2$ and range is $(0,oo)$

In the given function $p(x)=sqrt(3/(x-2))$ , you cannot have a negative number in the square root. Further, you cannot have $x-2=0$ .

Hence domain is $x>2$ .

When $x>2$ as $x->oo$ , $p(x)->0$ and as $x->2$ , $p(x)->oo$ ,

hence range is $(0,oo)$

The graph of $p(x)$ appears as follows:

graph{sqrt(3/(x-2)) [-6.54, 13.46, -2.44, 7.56]}

How do you find the domain and range of p(x) = sqrt{3/(x - 2)}p(x) = sqrt{3/(x - 2)}?