10. (The 19th "Hope Cup" Grade 1 High School Second Test) Given that $k$ is a positive number, and the function $f(x)$ is an odd function on $\mathbf{R}$, if the solution set of the inequality $f(x)>k x$ is $\{x \mid x<-4$ or $0<x<4\}$, then the solution set of the inequality $f(|x|) \leqslant k|x|$ is
A. $\{x \mid x \geqslant 4\}$
B. $\{x|| x \mid \leqslant 4\}$
C. $\{x|| x \mid \geqslant 4$ or $x=0\}$
D. $\{x \mid x \geqslant 4$ or $x \leqslant 0\}$
10. C Since $|x| \geqslant 0$, and when $x \geqslant 0$, the solution set of $f(x)>k x$ is $(0,4)$. Therefore, the solution set of $f(x) \leqslant k x$ is $\{0\} \cup[4,+\infty)$, hence $|x| \in\{0\} \cup[4,+\infty)$, so the answer is $\mathbf{C}$.