The function $f: x \mapsto -x^2 + 6x - 5$ has domain $x \geq m$, with $m$ as a constant.
(a)[3]
Express $-x^2 + 6x - 5$ using the form $(x + b)^2 + c$, where $b$ and $c$ are constants.
(b)[1]
State the least value of $m$ for which $f$ is one-one.
(c)[4]
For the situation where $m = 5$, find an expression for $f^{-1}(x)$ and state the domain of $f^{-1}$.
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