Question 755537
No it does not express y as a function of x.  You did actually find part of the equation in the form of y as a function of x.  The original equation ALSO has a lower branch which is also a function of x.  


Taking square root of {{{y^2=x+2}}}, you have BOTH of these:
{{{y=sqrt(x+2)}}} AND {{{highlight(y=-sqrt(x+2))}}}


Consistant with that, {{{ x-y^2=-2}}} IS NOT A FUNCTION.


A reason it is not a function is because for all but one value of x, each value of x gives more than one value of y.

{{{graph(300,300,-3,9,-6,6,sqrt(x+2),-sqrt(x+2))}}}