Question

Scott is walking. Dt), given below, is his distance in kilometers from Glen City after t hours of walking. D(t) = 15.5-50 Complete the following statements. Let D be the inverse function of D. Take x to be an output of the function D. (a) Which statement best describes D™G)? xs ? His distance from Glen City (in kilometers) after he has walked x hours. The ratio of the amount of time he has walked in hours) to his distance from Glen City (in kilometers), X. The reciprocal of his distance from Glen City (in kilometers) after walking x hours. The amount of time he has walked in hours) when he is x kilometers from Glen City. (6) D='(x) = 0 co D**(8.5) - 0

Answer 1

(a) Fourth option is correct

(b) D^-1(x)=3.1-x/5

(c) D^-1(8.5)=1.4 hours

amoun Түм Since D(t) = 15.5-5€ is the function of time which gives the walking distance of la scoff if you put the walking time, Therefore the inverse function D ) will give you the walking time if you put walking distance x into 01(x), Hence the answer for quation (a) is the 4th option, ie. "The amount of time he walked I (in hours) when he is a kilometer from Glen city" (6) Let Dit) = x = 15:5-5t => 5t = 15.5.- x > t = 15.5=X 158 - x .* t = 3.1-x Thus the inverse function is TOGE) = 3:1-7 3.1 (C) D"05) = 3.1-0.5 = 3.1 -1.7 TD-1 (8-5) = 114 hours.