文[1]对文[2]中的定理推广为:若方程x+f(x)=m和x+f-1(x)=m的根分别为a,b.则a+b=m.经类比探讨,笔者得到如下结论.定理若方程x·f(x)=m和x·f-1(x)=m分别有唯一根a,b.则a·b=m.该定理的证明用到类似文[2]的引理:若函数y=f(x)与y=g(x)图象的交点为P(x0,y0),则点P′(y0,x0)一定是函 The paper [1] generalizes the theorem in [2]: if the roots of the equations x+f(x)=m and x+f-1(x)=m are a, b, then a+b=m By analogy, the author got the following conclusion. Theorem if the equations x·f(x)=m and x·f−1(x)=m respectively have unique roots a, b. then a·b=m. Prove that we use a lemma similar to [2]: If the intersection of the function y=f(x) and the y=g(x) image is P(x0,y0), then the point P’(y0,x0) must be letter