Monotonous functions/Composition/Parity/Exercise

Let

$f_{1},\ldots ,f_{n}\colon \mathbb {R} \longrightarrow \mathbb {R}$

be functions, which are increasing or decreasing, and let ${}f=f_{n}\circ \cdots \circ f_{1}$ be their composition. Let ${}k$ be the number of the decreasing functions among the ${}f_{i}$'s. Show that if ${}k$ is even, then ${}f$ is increasing, and if ${}k$ is odd, then ${}f$ is

decreasing.

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