My function is defined as \begin{align*} f:\left[-\frac{3}{2},\infty\right) &\to [0,\infty),\\ x&\mapsto\sqrt{2x+3}. \end{align*}
We notice that $f$ is strictly increasing and that it is invertible.
Proposition: $$f_{n+1}(x)=x \Longleftrightarrow f(x)=x$$ for any $n\in\mathbb N^*$, where $$f_{n+1}=f\circ f\circ \cdots \circ f, \quad \forall n \in \mathbb{N}^*$$ and $f_{n+1}$ has the same domain and codomain as $f$.
The thing is that the proposition seems obvious as it happens for any $n$, including $n=1$, but I don't understand why it mentions the monotony too. Is there something that I might have missed?
Thanks in advance!