In a thermal expansion of water lab, a glass bottle of water is cooled to 0 degrees and the water level is observed as the temperature rises. there is a decrease in water level from 0 degrees to 4 degrees. then, at about 15 degrees when the bottle is placed in a warm bath (30 degrees), why is there another small and almost instant decrease in the water level when placed in the warm bath before it starts to rise again?

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 .