How do you find the domain and range of #g(t) = sqrt(3-t) - sqrt(2+t)#?

1 Answer
May 17, 2018

Answer:

Domain is #-2<=t<=3# i.e. #[-2,3]# and range is #-sqrt5<=g(t)<=sqrt5# i.e. #[-sqrt5,sqrt5]#

Explanation:

In the function #g(t)=sqrt(3-t)-sqrt(2+t)#

we can only have a non-negative number under square root sign.

Hence we ought to have #3-t>=0# i.e. #t<=3# and #2+t>=0# i.e. #t>=-2#

and hence domain is #-2<=t<=3#

As #t# takes value #-2#, #g(t)=sqrt5# and as #t# takes value #3# #g(t)=-sqrt5#

Hence range is #-sqrt5<=g(t)<=sqrt5#

graph{sqrt(3-x)-sqrt(2+x) [-6, 6, -3, 3]}