Question 164428
{{{f(x)=-sqrt(1-x)}}} Start with the given function



{{{y=-sqrt(1-x)}}} Replace f(x) with y



{{{x=-sqrt(1-y)}}} Switch x and y



{{{-x=sqrt(1-y)}}} Multiply both sides by -1



{{{x^2=1-y}}} Square both sides.



{{{x^2+y=1}}} Add y to both sides



{{{y=1-x^2}}} Subtract {{{x^2}}} from both sides



{{{y=-x^2+1}}} Rearrange the terms.



So the inverse function is {{{f^-1(x)=-x^2+1}}} 


Note: the domain and range of {{{f(x)=-sqrt(1-x)}}} is {{{x<=1}}} and {{{y<=0}}}


So this means that the domain and range of {{{f^-1(x)=-x^2+1}}} is {{{x<=0}}} and {{{y<=1}}}