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

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Answer 1 · 2018-05-17T06:01:24

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

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]}