Function Transformation and Simplification

Very Hard Algebra Functions

Consider the function defined as:

$$ f(x) = x^4 - 4x^2 + 4 $$

Let another function be defined as:

$$ g(x) = f(x + 1) - f(x) $$

What is the simplified expression for $$ g(x) $$?

$$ g(x) = 4x^3 + 6x^2 + 4x $$

$$ g(x) = 4x^3 - 6x^2 + 4x $$

$$ g(x) = 4x^3 + 6x^2 - 4x $$

$$ g(x) = 4x^3 - 6x^2 - 4x $$

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