A) assume uniform, isothermal, non-rotating jeans collapse. what radius gas cloud would a browm dwarf of mass 0.07 solar masses and temperature 1000k form from? assume u=1
b) the smallest observed molecular clouds (blok globules) are approximately 1000 a. u. in radius, with a wide range in density and t. why is this a problem for part (a) above? what additional physics must the model include to allow brown dwarfs to form via gravitiational collapse? describe the chain of events.

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 .