Square root function?

Algebra Level 4

Consider a function \(f:\mathbb{N} \to \mathbb{R}\), \(y=f(x)\), which satisfies \(f(n) = \sqrt{f(n+1)}+c\), where \(c \in \mathbb{R}\) is a constant. If \(f(x)\) is not a constant function and \(c \neq 0\). Then which of the following about \(f(x)\) can be true?

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