The function f is such that $f\left( x \right) = 3 - 4{\cos ^k}x$, for $0 \leqslant x \leqslant \pi $, where $k$ is a constant.
a) In the case where $k = 2$,
(i) find the range of f,
(ii) find the exact solutions of the equation $f\left( x \right) = 1$.
b) In the case where $k = 1$,
(i) sketch the graph of $y = f\left( x \right)$,
(ii) state, with a reason, whether f has an inverse.
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