Relation between angular and and linear variable
explain

The Relations between Linear and Angular Variables: Each of the angular variables θ, ω, and α is related to its corresponding linear variable x, v, and at by factor R, the radius of rotation. One type is at , the tangential acceleration that is responsible for the change in the magnitude of the linear velocity, v.

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 .