The company you work for needs you to design a bumper for a car with a mass of 1500 kg. The impact force must be less than 200 kN at a speed of 50 km/h when the car crashes into a concrete wall. If your design is successful, how long will it take the car to come to a complete stop after the impact?

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 .