Charlie is playing with his daughter torrey in the snow. she sits on a sled and asks him to slide her across a flat, horizontal field. charlie has a choice of (a) pushing her from behind by applying a force downward on her shoulders at 30^\circ below the horizontal (fig. a), or (b) attaching a rope to the front of the sled and pulling with a force at 30^\circ above the horizontal (fig. b). which would be easier for him and why?

b

Explanation:

Pulling up with the rope would decrease the frictional force, pushing down would increase the frictional force.

seeing the graph would

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 .