If f(x)=−x|x|1+x2,  then f−1(x)  equals

Let y=f(x)={−x21+x2,        if  x≥0x21+x2,         if  x<0 f−1(y)={−y1+y,    y<0−y1−y, y>0 Or f−1(x)={−x1+x,  x<0−x1−x,  x>0f−1(x)=−{(−x1+x),    x<0(−x1−x),     x>0=−(sgnx)|x|1−|x|