A mass gains a speed of 28.2 cm/s when it is released from rest at the free end of a spring that is compressed by 3.20 cm horizontally. If the mass is now connected to the free end of the spring to form a mass-spring system, what is the period of this harmonic oscillator?

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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 .