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ISI-2017 MMA

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Let $S \subseteq R$. Consider the statement:

"There exists a continuous function $f:S \rightarrow S$ such that $f(x) \neq x$ for all $x$ belongs to $S$."

This statement is false if $S$ equals

  1. $[2,3]$
  2. $[2,3]$
  3. $[-3,-2] \cup  [2,3]$
  4. $(-\infty \text{ to} +\infty)$

 

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