I am stuck on the following problem that says:
Let $\,\displaystyle f \colon [0,1] \to [0,1]$ be continuous and $\,f(0)=0,f(1)=1.$ Then $f$ is necessarily
injective ,but not surjective
surjective,but not injective
I have to determine which of the following options is correct. Can someone help? Thanks and regards to all.