Question 891757
f(x), no restrictions.  ALL REAL Numbers for domain.


Viewing as for standard form, {{{f(x)=2(x-0)^2+2}}} with minimum at y=2.
Range is {{{f(x)>=2}}}.


f(x) does not really have an inverse; unless you specify for the left and right branches of f around x=0.


LEFT BRANCH OF f:
Domain is -infintity to 0, 
Range is from 2 to +infinity.
INVERSE OF LEFT BRANCH of f:
Domain is from 2 to +infinity.
Range is -infinity to 0.
THE ACTUAL FUNCTION OF INVERSE OF LEFT BRANCE OF f:
----This will be the lower branch for {{{y^2+2=x}}} when solved for y.  You want the negative branch.
---- See how "y" and x are switched places.
---- {{{y^2=x-2}}}
{{{y=0+- sqrt(x-2)}}}
and you need for here, the "minus" branch:  {{{f^-1(x)=-sqrt(x-2)}}}.


You can find the inverse for the right branch of f.