if `a,b` are two positive numbers such that ` f(a+x)=b+[b^3+1-3b^2f(x)+3b{f(x)}^2-{f(x)}^3]^(1/3)` for all real `x`, then prove that `f(x)` is peroidic and find its peroid?

Explanation

` f(a+x)=b+[b^3+1-3b^2f(x)+3b{f(x)}^2-{f(x)}^3]^(1/3)`

` f(a+x)=b+[1+{b-f(x)}^3]^(1/3)`

` f(a+x)-b=[1+{b-f(x)}^3]^(1/3)`

thus,

`u(a+x)=[1-(u(x))^3]^(1/3)->(1)`

And,

`u(2a+x)=[1-(u(x+a))^3]^(1/3)`

So,

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