deg of composition on supersingular curve

Question

Let we have supersingular curve $E(\bar{\mathbb{F}_q})$. Let we have algebraic function $f \in \bar{\mathbb{F}_q}(E)$ with div($f) = \sum_{i=0}^{i=n}n_iP_i$. Then div$(f) \circ [q] = \sum_{i=0}^{i=n}n_iQ_i$ where $[q]Q_i = P_i$ ($Q_i$ is unique because $E$ is supersingular). So deg$(f)$ = deg$(f)\circ[q]$. Is it correct reasoning?