Question 936327
The domain of f is the range of its inverse.
The range of f is the domain of its inverse.


The vertex of f and the sign of leading coefficient tells you something about range for f.


The quick way to find the inverse of f is to switch function and x roles:
{{{x=-3y^2+5}}}
{{{-3y^2=x-5}}}
{{{y^2=(x-5)/(-3)}}}
{{{y^2=-(x-5)/3}}}
{{{y=0+- sqrt(-(x-5)/3)}}}, the inverse of f.
Each branch is a separate function; when both branches are put together, that is not a function.



f(x)
{{{graph(300,300,-10,10,-10,10,-3x^2+5)}}}


The negative branch of inverse of f
{{{graph(300,300,-10,10,-10,10,-sqrt(-(x-5)/3))}}}


The positive branch of inverse of f
{{{graph(300,300,-10,10,-10,10,sqrt(-(x-5)/3))}}}