An object is placed on a common central axis of two thin lenses. The distance from the object to the first lens is 19 cm. The distance between the two lenses is 35 cm. The first lens is a converging lens with a focal length of 9.9 cm. Thesecond lens is a diverging lens with a focal length of 9.0 cm. What is the magnification of the system?

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 .