Let the function

$f\left(x\right)=3x^2-4x+8\log \left(1+\left|x\right|\right)$ be defined on the interval [0, 1]. The even extension of f(x) of the interval [-1, 1] is

$f\left(x\right)=-f\left(x\right)$      $x\in [0,1]$

          $-f(-x)$    $x\in [-1,0]$

$f\left(x\right)=3x^2-4x+8\log \left(1+\left|x\right|\right)x\in [0,1]$

$f\left(x\right)=3x^2+4x+8\log \left(1+\left|x\right|\right)x\in [-1,0]$

$\therefore f\left(x\right)=3x^2-4\left|x\right|+8\log \left(1+\left|x\right|\right)x\in [-1,1]$