Assume a three-phase, unity power actor load of 100 MVA with VLL of 69 kV is connected to a source through the below network. Convert the two impedances to per unit. Use a per unit three-phase 100 MVA base, a line-to-line 138 kV voltage base on the left side of the transformer and a line-to-line 69 kV voltage base on the right side.

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 .