Find the inverse function [math]g(x)[/math] of the function [math]f(x)=1−\sqrt{x}[/math]. Then verify algebraically that the two functions are inverses.
[list=1] [*]Find the possible inverse function [math]g(x)[/math] of the function [math]f(x)=1−\sqrt{x}[/math]. [*]Find the composition [math]g(f(x))[/math] and verify that it simplifies to [math]x[/math]. [*]Find the composition [math]f(g(x))[/math] and verify that it simplifies to [math]x[/math]. [/list]