Question 880499
Be aware that the inverse of g is not a single function.  g^-1(0) might be undefined, have one value or might have two values.


{{{2(x^2+2x+1)}}}
{{{2(x+1)^2}}}
{{{g(x)=2(x+1)^2}}}
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If y is the inverse, then {{{x=2(y+1)^2}}}
{{{x/2=(y+1)^2}}}
{{{y+1=0+- sqrt(x/2)}}}
{{{y=-1+- sqrt(x/2)}}}
Rationalize the denominator if desired
{{{y=-1+- sqrt(2x)/2}}}
Decide which branch you want for {{{g^-1(x)}}}.