Consider a cylindrical distribution of charge. the cylindrical surface is infinite in length with radius rc and uniform charge distribution rs [c/m2] on its surface. determine the e field at a distance r away from the center of the cylinder. just set up the problem to where all that is left is integrations and math. don't perform the integrations. do not use a gaussian surface to solve this problem.

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 .