Question 967940
Maybe you meant {{{f(x)=x^2+3}}}, for {{{x<0}}} ?
You want the inverse of f.


Let g(x) be the inverse function of f(x).
{{{g(f(x))=f(g(x))=x}}}.


{{{(g(x))^2+3=x}}}
{{{(g(x))^2=x-3}}}
{{{g(x)=0+- sqrt(x-3)}}}, for {{{g(x)<0}}} only.  The negative branch of this is required; so this means what the really needed answer is:


{{{highlight(g(x)=-sqrt(x-3))}}}  AND  {{{x>=3}}} if staying with real number solutions.