According to avogadro's law, the volume of a gas is inversely related to the number of moles at constant temperature and pressure the volume of a gas is inversely related to the number of moles at standard temperature and pressure the volume of a gas depends only on the temperature and pressure the volume of a gas depends only on the number of moles in the sample the volume of a gas is directly related to the number of moles at constant temperature and pressure

Here by ideal gas equation we have

PV = nRT

so here if

So we can say pressure , volume and temperature ratio is same then number of moles must be same

for

So number of moles is directly proportional to product of volume and pressure of the gas and inversely proportional to temperature of the gas

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 .