已知函数f（x）=2﹣2cos²（$\frac{\mathrm{\pi }}{4}$+x）﹣$\sqrt{3}$cos2x

（1）求函数f（x）在x∈0，π时的增区间；

（2）求函数f（x）的对称轴；

（3）若方程f（x）﹣k=0在x∈$\frac{\mathrm{\pi }}{4}$，$\frac{\mathrm{\pi }}{2}$上有解，求实数k的取值范围．

I will never forget my first English class. It is very interesting. It's the first class in the morning. The teacher goes into the classroom with a smile on his face. At the beginning, he makes a self-introduction(自我介绍). And he tells us that his English name is John. Then he asks all of us to think of English names for ourselves. We are very excited(兴奋的) to find a good name. Then he asks us to write our names down on a piece of paper. I think about my English name for a long time. Then I come up with(想出) a beautiful name ---Shirley. All the students write their names down and give the paper to the teacher. When the teacher calls “Shirley” to answer his question, three girls stand up at the same time.

① $\frac{5}{7}+\frac{3}{10}=\frac{3}{10}$ ____ $\frac{5}{7}$

② $\frac{3}{8}$ ____ $\frac{5}{6}$ $=\frac{5}{6}$ ____ $\frac{3}{8}$

③ $\frac{1}{3}+\frac{5}{9}+\frac{4}{9}=\frac{1}{3}+$ ( $\frac{5}{9}$ ____ $\frac{4}{9}$ )

④ $\frac{3}{8}+\frac{1}{10}+\frac{5}{8}+\frac{9}{10}=$ ( $\frac{3}{8}$ ____ $\frac{5}{8}$ )+( $\frac{1}{10}$ ____ $\frac{9}{10}$ )