Given an alphabet $\Sigma$, consider the operation $f : \Sigma^* → \Sigma^*$, defined as $$ f(w) = w_n \circ w_{n−1} \circ w_{n−2} \circ \cdots \circ w_1, $$ where $w = w_1 \circ w_2 \circ w_3 \circ \cdots \circ w_n$. $f$ is extended to apply to a given language $L$ as follows: $$ f(L) = \{f(w) \mid w \in L\}. $$
Prove or disprove the claim that the class of context-free languages is closed under $f$.