Domains Were Never This Tough!!!

Algebra Level 4

A function f is non-negative and defined on an appropriate subset of Real Numbers . If

$${ x }^{ 2 }f\left( x \right) \quad +\quad f(1-x)\quad =\quad 2x-{ x }^{ 4 }$$

is true for all x on the domain , then find largest interval of values of x as [a,b]

What is The Value of [100(a+b)]

[x] represents the greatest integer function

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