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Let the function \(f\) be defined by $$\Function{f}{[1, \infty)}{[2, \infty)}{x}{(x-1)^2 + 2}$$
  1. State the domain and range of \(f\).
  2. Find an expression for \(f^{-1}(x)\).
  3. State the domain and range of \(f^{-1}\).

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