Question 1046583
Use x,y.
{{{y=2(3x+1)^2}}}
Interchange x and y and solve for the new y. 
That new y is the inverse.
{{{x=2(3y+1)^2}}}
{{{x/2=(3y+1)^2}}}
{{{3y+1=0 +- sqrt(x/2)}}}
{{{3y=-1 +- sqrt(x/2)}}}
{{{y=-1/3 +- (1/3)sqrt(x/2)}}}
{{{f^(-1)(x)=-1/3 +- (1/3)sqrt(x/2)}}}
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*[illustration sn2.PNG].