A large goose lands in a lake and bobs up and down for a short time. A fisherman notices that the first wave crest created by the goose reaches the shore 7.3 s after the goose first contacts the water. The distance between two wave crests is 65 cm, and in 1.9 s he sees four wave crests hit the shore. How can the fisherman use these observations to determine how far from the shore the goose landed?

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

the answer is 100. i just did this lesson and got a 100% on it. : )

-fishtank