An even polynomial function f(x) satisfies a relation f2x1-f12x+f16x2y=f-2-f4xy∀x,y∈R-0   and  f4  =-255,  f0=1.   Then the value of f(2) is________

We   have   f2x-  f2xf12x+f16x2y=f-2-f4xyReplacing   y  by  18x2,  we   getf2x-f2x12x+f2=f-2-f12x∴   f2x+f12x=f2xf12x     As  fx  is  even∴  f2x=1±2xnor   fx=1±xnNow,  f4=1±4n=-255     GivenTaking negative sign, we get 256=4n   or   n=4Hence,  fx=1-x4,  which is an even functionTherefore, f2=-15.