$f(t^2 +t +1) = t$ For $t^2+t+1=m$ so $t = 1/2 (\sqrt{4 m - 3} - 1)$ Then; $$ f(t)= 1/2 (\sqrt{4m-3} - 1) $$

oralayhan wrote: $t = 1/2 (\sqrt{4 m - 3} - 1)$ how do you get this?

you see find that the inverse function for x^2+x+1 is the actual function.