如图，四棱锥P﹣ABCD中，侧面PAD为等边三角形且垂直于底面ABCD，AB=BC= $\frac{1}{2}$ AD，∠BAD=∠ABC=90°，E是PD的中点．

（Ⅰ）证明：直线CE∥平面PAB；

（Ⅱ）点M在棱PC 上，且直线BM与底面ABCD所成角为45°，求二面角M﹣AB﹣D的余弦值．

I w____ to Qingdao with my parents last summer holiday. We t____a plane there. We went to the beach. It was very b ____. I like swimming very much. I s____in the sea. My mum took many p____ there. We had a good time.

设函数f（x）对任意x∈R，都有f（2x）=a•f（x），其中a为常数．当x∈1，2）时，$f\left(x\right)=\sin \left(\frac{\mathrm{\pi }}{2}x\right)$．

（1）设a＞0，f（x）在x∈4，8）时的解析式及其值域；

（2）设﹣1≤a＜0，求f（x）在x∈1，+∞）时的值域．