Embarking on a road trip, you hope to average a speed of 90.0 km/hr. Driving through bad weather, you finally reach the midpoint (half the distance) of your trip, but realize that you have only been averaging 5.0 X 10^1 km/hr. How fast would you have to drive the second half of the trip to keep your desired arrival time? *

Explanation:

average speed = 90 km / hr

Let the total distance be 2 d .

time required to cover the time = 2 d / 90

time taken   to cover distance d at 50 km /h = d / 50

time required to cover the  nd half = 2 d / 90 -  d / 50

.02222 d  - .02 d = .002222 d

speed required = d/2 / .002222d

1 / 2 x .002222

= 225 km /h .

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 .