设f(x)=x(ex-1)/ex+1，证明：f(x)是偶函数．
证明：f(x)的定义域是(-∞，+∞)，并且 f(-x)=-x(e-x-1)/e-x+1=-x•(1/ex-1)/(1/ex+1) =-x•[(1-ex/ex)/(1+ex)/ex] =x(ex-1)/(ex+1)=f(x) 所以f(x)为偶函数．
设f(x)=x(ex-1)/ex+1，证明：f(x)是偶函数．
证明：f(x)的定义域是(-∞，+∞)，并且 f(-x)=-x(e-x-1)/e-x+1=-x•(1/ex-1)/(1/ex+1) =-x•[(1-ex/ex)/(1+ex)/ex] =x(ex-1)/(ex+1)=f(x) 所以f(x)为偶函数．
