At what height in kilometers above the surface of the Earth is there a 7% difference between the approximate gravitational force mg and the actual gravitational force on an object

There is a 7 % difference between the approximate gravitational force and the actual gravitational force at a height of 240 kilometers.

Explanation:

We can calculate gravity as a function of mass of the Earth (), measured in kilograms, radial distance from center of the planet (), measured in meters, and gravitation constant (), measured in newton-square meters per square kilogram:

(Eq. 1)

And we solve the equation for :

(Eq. 1b)

If we know that , and , the radial distance from the center of the Earth is:

The height above the surface of the Earth is the difference between the value above and the radius of the planet. That is:

()

There is a 7 % difference between the approximate gravitational force and the actual gravitational force at a height of 240 kilometers.

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 .