The function $f$ is one-one and is given by $f(x) = (x - 2)^2 + 2$ for $x \geq c$, where $c$ is a constant.
(i)[1]
State the least possible value of $c$.
(ii)[3]
Find an expression for $f^{-1}(x)$ and state the domain of $f^{-1}$. For parts (ii) and (iii), take $c$ to be $4$.
(iii)[5]
Solve the equation $f f(x) = 51$, and give your answer in the form $a + \sqrt{b}$.
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