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

1 Answer
Nov 4, 2017

Answer:

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]}