Aplastic tube placed from the ventricles of the brain to the peritoneal cavity in order to continuously remove excess cerebrospinal fluid is called a shunt.

ventriculoperitoneal      

Explanation:

A VP or ventriculoperitoneal shunt is a medical equipment or a device which is used to relieve pressure from the brain that is caused by the accumulation of fluid in the brain. Ventriculoperitoneal shunting is a medical procedure that is primarily used to treat a condition  known as hydrocephalus. This condition occurs when the more cerebrospinal fluid (CSF) gets collected in the  ventricles of the brain than required.

Hence the answer is ---

ventriculoperitoneal      

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 .