Let $f(x)$ is continuous in $[0,1]$, differentiable in $(a,b)$, such that $f(0)=g(0)=f(1)=0$, $g'(x)\neq0$.
I have no idea about it, but I can post some link which I think is useful.
This is a question of a real-analysis book which named 'Mathematical analysis course'(Author:Shi Jihuai,Chang Gengzhe).
Book Name:数学分析教程(Mathematical analysis course)
Author: 史济怀 常庚哲
When there are two parameters in question,we can express them by a node which associated with both.
And then we can remove the node by some operations.For this question, We can see the answer of I posted.
I want to get a proof,and a way to solve two-parameter($\xi,\eta$) question