 #1
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 14
Homework Statement:

Let function ƒ be Continuous in the compact interval [a,b].
if f(a)=f(b), then f is not Injective in the open interval (a,b)
Relevant Equations:
 Rolle's theorem
It all makes sense to me, but I don't know how to formalize it nicely.
I wanted to divide it into two cases.
First case where f is fixed in the segment.
And a second case where f is not fixed in the segment.
But I don't know how to prove it for the case where f i is not fixed
I wanted to divide it into two cases.
First case where f is fixed in the segment.
And a second case where f is not fixed in the segment.
But I don't know how to prove it for the case where f i is not fixed