A vehicle accelerates from 0 to 30 m/s in 10 seconds on a straight road, then travels 15 seconds at a constant velocity. Next it slows down, coming to a stop in 5 seconds. The car waits 10 seconds, and then backs up for 5 seconds accelerating from 0 to -10 m/s. Draw a graph showing the vehicle's velocity vs time by following these steps. What is the velocity of the vehicle at 0 seconds? 0 m/s Click or tap the graph to plot this point.

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explanation:

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 .

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