Question 973118
You want the lower branch of the inverse.  {{{y<-1}}} is what you want.


{{{4y^2+4y+1=x}}}
{{{4(y^2+y+1/4)=x}}}
{{{4(y+1/2)^2=x}}}
{{{(y+1/2)^2=x/4}}}
{{{y+1/2=0+- sqrt(x)/2}}}
{{{y=-1/2+- sqrt(x)/2}}}


Domain x<-1  of the given function corresponds to the lower branch of the inverse function:
{{{highlight(y=-1/2-sqrt(x)/2)}}}, this inverse.



Your given function
{{{graph(300,300,-5,5,-5,5,4x^2+4x+1)}}}
graph is not perfect but includes the whole function.
x less than -1 was specified.


The inverse needed
{{{graph(300,300,-5,5,-5,5,-1/2-sqrt(x)/2)}}}
graph not perfect.  y less than -1 is the range wanted.