\(2f\left(2x\right)+f\left(1-2x\right)=12x^2=3.\left(2x\right)^2\) (1)
\(\Rightarrow2f\left(1-2x\right)+f\left(2x\right)=3\left(1-2x\right)^2\) (2)
Lấy \(\left(2\right)-2.\left(1\right)\) ta được:
\(-3.f\left(2x\right)=3\left(1-2x\right)^2-24x^2\)
\(\Rightarrow f\left(2x\right)=4x^2+4x-1=\left(2x\right)^2+2.\left(2x\right)-1\)
\(\Rightarrow f\left(x\right)=x^2+2x-1\)