Consider the function f(x) = x³ - 5x² + 6x-3+1, x>0 The function f(x) = x³- 5x² + 6x − 3 + 1½-½, x > 0, models the path of a river, as shown on the following map, where both axes represent distance and are measured in kilometres. On the same map, the location of a highway is defined by the function g(x) = 0.5(3)¯* +1. 4 north river 3. 2 1 Orangeton -1 highway 0 2 x 4 6 7 8 9 -2- The origin, O (0, 0), is the location of the center of a town called Origintown. A straight footpath, P(x), is built to connect the center of Origintown to the river at the point where x = 1 State the domain of P(x). Bridges are located where the highway crosses the river. What are the coordinates of the bridges? A straight road is built from the center of Origintown, due north, to connect the town to the highway. Find the distance from the center of Origintown to the point at which the road meets the highway. This straight road crosses the highway and then carries on due north. State whether the straight road will ever have a bridge that crosses the river. Justify your answer.