Question

Question 6. (7 points) Consider the function S(,y) = cos(In(a + y)). a) Find the domain and range. b) Sketch the domain. c) On a separate graph, sketch three level curves.

Answer 1

& fimy) finy) = Coslan Inty)) Since en is defined only if no and cost is defined ther. finy) = Costuninty)) is defined for a+y>0. 4 f (my) = cos (anin+y)) xtyzo > Un luty) ER » Costchn Cary)) E [-1, 1] Bomain = {(my) JR2 | *+9>0} Range = [-% nty = 0 @ ut > Domain » y=-x --rty20

© Let fla,y) =c » cool cesta+y)) = C. c=1 * cos(clointy)) = 1 - un luty)) = 2n1 ne z C=0 → Cos Icon ruty)) = 0 => un Inty) = (2n+i) ne 24 - nty = e(2n+1)/2 ne z C=- = so Iminty)) = (21+1 nez un (n+y) = kn+1) - nty = e entit Put n=o in each then level curves are nty=et nty = et/2 aty = 1