文[1]给出了一个定理:若f(x)是[a,b]上的增函数,x+f(x)=m,x+f-1(x)=m的两根分别为a,b,则a+b=m.文[2]将这个定理推广为:若方程x+f(x)=m,x+f-1(x)=m的两根分别为a,b,则a+b=m.文[3]再次将其类比推广为:若方程xf(x)=m,xf-1(x)=m分别有唯一根a,b,则ab=m.本文进一步对这类问题进行探 A theorem is given in [1]: if f(x) is an increasing function on [a,b], x+f(x)=m and x+f-1(x)=m are respectively a,b, then a+b=m. [2] generalize this theorem: if the equation x+f(x)=m, two roots of x+f-1(x)=m are respectively a,b , then a + b = m. Text [3] again extended its analogy to: If the equation xf (x) = m, xf-1 (x) = m have a unique root a, b, then ab = m. Further explore these issues