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Let \(f\) be the function defined by:$$ f(x) = \sqrt{x^3 - 1} $$
  1. Give the composition scheme of the function \(f\).
  2. Determine the domain of definition of the function \(f\), denoted \(D_f\).
  3. Study the variations of \(g : x \mapsto x^3 - 1\) and construct its table of variations on \(\mathbb{R}\).
  4. Deduce the table of variations of \(f\).

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