已知符号函数$sgnx=\left\{\begin{array}{l}\begin{array}{c}1,x>0\\ 0,x=0\\ -1,x<0\end{array}\\ \end{array}\right.$ $f\left(x\right)$是$R$上的增函数，$g\left(x\right)=f\left(x\right)-f\left(ax\right)\left(a>1\right)$，则

$sgn\left[g\left(x\right)\right]=sgnx$ $sgn\left[g\left(x\right)\right]=-sgnx$ $sgn\left[g\left(x\right)\right]=sgn\left[f\left(x\right)\right]$ $sgn\left[g\left(x\right)\right]=-sgn\left[f\left(x\right)\right]$