Let f:[-1,1]-->R be a continuous function such that f(-1)=f(1). Prove that there exists x Є [0,1] such that f(x)=f(x-1).
We consider g(x)=f(x)-f(x-1) defined on [0,1].
Since f:[-1,1]-->R is a continuous function, then g is also a continuous function.
Now we check g(0) and g(1). Since ...
A proof involving continuous functions is provided.