An ideal gas may be taken from one state to another state with a different pressure, volume, and temperature along several different paths. Quantities that will always be the same for procesa, regardless of which path is taken, include which of the following? I The change in internal energy of the gas. II The amount of heating between the gas and its surroundings. III. The work done by the gas.(A) I only(B) II only (C) I and III only (D) II and IIl only

the first, second, and fifth options

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 .