If  fx=4-x2+x2-1, then the maximum value of fx2  is __________

Let  x2=4  cos2θ+sin2θ.   Then            4-x2=3sin2θ  and    x2-1=3cos2θ∴    fx=3  sinθ+3cosθor     ymin=3  and  ymax  =312+12=6Hence,    range    of   fx  is   3,6.Hence,   maximum   value   of   fx2  is   6.