On the first part of a journey, a motorcyclist travels for 1.5 hours at a speed of 65 miles per hour. On the second part of the journey, the motorcyclist then travels for 45 minutes at 50
miles per hour. What was the total distance travelled by the motorcyclist?

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 .