Paper 1 May/June 2011 MATHEMATICS (9709/13) A Levels
لطفا برای اطمینان از عملکرد و تجربه بهتر از مرورگرهای مدرن و به روز مانند کروم یا فایرفاکس استفاده کنید.

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.