对于函数f（x），若∀a，b，c∈R，f（a），f（b），f（c）为某一三角形的三边长，则称f（x）为“可构造三角形函数”．已知函数f（x）=$\frac{e^x+t}{e^x+1}$是“可构造三角形函数”，则实数t的取值范围是（　　）

根据短文内容及首字母提示完成短文。

    My name is John. I am 13 years old. My b ____is 1st October and I was b____ in Nanjing. I live with my f____ in Shanghai. I have a t____ brother. I am s____ and I w____ glasses. I am good at English. I like playing football. I play football in the football f____. I also like c____ games. In the evening, I do my homework carefully. My father r____ newspapers. My mother c____dinner for us. My brother reads Chinese books every day.