Given that \(f: S \rightarrow R\) is said to have a fixed point at \(c\) of \(S\) if \(f(c)=c\).
Let \(f:[1, \infty) \rightarrow R\) be defined by \(f(x)=1+\sqrt{x}\). Then
(A) \(f\) has no fixed point in \([1, \infty)\)
(B) \(f\) has unique fixed point in \([1, \infty)\)
(C) \(f\) has two fixed points in \([1, \infty)\)
(D) \(f\) has infinitely many fixed points in \([1, \infty)\)