The spring is suspended vertically and we use a standard ruler to measure its equilibrium length while hanging. This equilibrium length is measured be L(subscript i)= 17.2 cm. Next, a series of hanging weights with known masses are suspended from the spring, which is allowed to reach equilibrium (that is, no acceleration; the spring is at rest). For each hanging weight, the total length of the spring is measured and recorded.

Draw a free-body diagram for one of the hanging weights while the system is in equilibrium.

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 .