Question 939682

{{{f(x)=4 + x^2}}}, {{{x>=0}}};   {{{g(x)=sqrt(x-4)}}} 

find inverse:

{{{f(x)=4 + x^2}}}.........{{{f(x)=y}}}

{{{y=4 + x^2}}}..........swap {{{x}}} and {{{y}}}


{{{x=4 + y^2}}}

{{{x-4=y^2}}}

{{{y=sqrt(x-4)}}}


{{{f^-1(x)=sqrt(x-4)}}} for {{{x>=0}}}

so, {{{g(x)=sqrt(x-4)}}} in inverse {{{f(x)=4 + x^2}}}


{{{ graph( 600, 600, -10, 10, -10, 10, 4 + x^2, sqrt(x-4)) }}}