∵f(x)=2/(a+x+b)
∴x≠-(a+b)
∴f(x)≠0
又 求出反函数f-1(x)=[2-x(a+b)]/x (x≠0)
且 由题 f-1(x)=f(x)
∴(2-x(a+b))/x = 2/(a+x+b)
∵ x≠0
∴a+b=0∵f(x)=a+2/(x+b)∴x≠-b∴f(x)≠a由题 求出反函数为f-1(x)=-b+2/(x-a) (x≠a)且 f-1(x)=f(x)∴ -b+2/(x-a)=a+2/(x+b)∴ a=-b∴a+b=-b+b=0