Let S ⊆ R.
Consider the statement:
"There exists a continuous function f:S -> S such that f(x) != x for all x belongs to S."
This statement is false if S equals
A) [2,3] B) (2,3] c) [-3,-2] union [2,3] D) (-infinity to +infinity)
I think the answer should be D because in -infinity to +infinity, f(x) will definitely be equal to x at some point but we want this to not happen as said in the question. Am I correct?