Given $$A = \left\{ {x:{\pi \over 6} \le x \le {\pi \over 3}} \right\}$$ and
$$f\left( x \right) = \cos x - x\left( {1 + x} \right);$$ find $$f\left( A \right).$$
Answer
$$\left[ {{1 \over 2} - {\pi \over 3}\left( {1 + {\pi \over 3}} \right),\,{{\sqrt 3 } \over 2} - {\pi \over 6}\left( {1 + {\pi \over 6}} \right)} \right]$$