Question

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

Answer 1

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

Explanation:

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]}