题目

Many cultures have different ideas about why people catch colds. For example in the United States, some people think that you can catch a cold if your feet get cold. So, mothers tell small children to wear warm boots in the winter. In other places, including parts of the Middle East, some people believe that strong winds cause colds. So, on trains and buses, people usually don’t like to sit next to open windows. In parts of Europe, some people think that wearing wet clothes will give you a cold. They say that after you go swimming, you should quickly put on dry clothes. Today, scientists kno已知二次函数f（x）满足f（x+1）-f（x）=2x且f（0）=1。（1）求f（x）的解析式； （2） 当x∈[-1，1]时，不等式：f（x）>2x+m恒成立，求实数m的范围；（3）设g（t）=f（2t+a），t∈[-1，1]，求g（t）的最大值。