ALPHA DIVISION

Question 114

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Question

Let

\Delta

be an operator such that

\Delta(f(x))=f(x+1)-f(x)

. Furthermore,

\Delta^1(f(x))=\Delta(f(x))

and for

n\geq 2, \Delta^n(f(x))=\Delta(\Delta^{n-1}(f(x)))

. Let

g(x)=\Delta(x^3)+\Delta((x-1)^3)

. Compute g(1).

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