Question 1031070
Only #23 for you.


Find inverse of f(x)=-2x^2+6 for x<=0;


Simple enough to exchange "y" and x.
{{{-2y^2+6=x}}}
{{{-2y^2=x-6}}}
{{{y^2=(1/2)(6-x)}}}
{{{y^2=-(1/2)(x-6)}}}
{{{y^2=(6-x)/2}}}
{{{y=0+- sqrt((6-x)/2)}}}  or  {{{f^-1(x)=0+- sqrt((6-x)/2)}}}.


When you look at the requested graph, you want to take the part that is for {{{y<=0}}}, because the inverse exchanged x and y.


Choose what you need from this RELATION  (which includes BOTH inverse function branches).
{{{graph(400,400,-8,8,-8,8,sqrt((6-x)/2),-sqrt((6-x)/2))}}}