5. Air enters a compressor operating at steady state with a pressure of 14.7 psia, a temperature of 80 F, and a volumetric flow rate of 18 ft3/s. The air exits the compressor at a pressure of 90 psia. Heat transfer from the compressor to its surrounds occurs at a rate of 9.7 BTU/hr per pound of air flowing. The compressor power input is 90 hp. Neglecting kinetic and potential energy effects, and modeling the air as an ideal gas, determine the exit temperature (F).

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 .