<s>[INST] This problem is designed to help you think about the properties of different types of mathematical functions. In the following, $f(x)$ is a continuous function defined for all real numbers. When $f$ is applied $n$ times to the value $x$, we denote the result by $f^n(x)$. For example, $f^3(x)$ means that $f$ is applied three times to the value $x$, or $f(f(f(x)))$. 

Suppose that $f(0) = 0$, and $f(1) = 1$. Which of the following statements about $f(x)$ MUST be true?[/INST]