Question 939683
to determine if {{{g}}} is the inverse of {{{f}}}, find the inverse of {{{f}}} first

{{{f(x)=1-x^2}}} .........recall that {{{f(x)=y}}}

{{{y=1-x^2}}} ...swap {{{x}}} and {{{y}}}

{{{x=1-y^2}}} ....solve for {{{y}}}

{{{x+y^2=1-y^2+y^2}}}

{{{y^2+x=1}}}

{{{y^2=1-x}}}

{{{y=sqrt(1-x)}}} or

{{{f^-1(x)=sqrt(1-x)}}} 

so, here we have two solutions: {{{f^-1(x)=sqrt(1-x)}}} and {{{f^-1(x)=-sqrt(1-x)}}}


since  {{{g(x)=-sqrt(1 -x )}}}, means {{{g(x)}}} IS  the inverse of {{{f}}}