(Canadian Senior Mathematics Contest 2020, Part A, Question 6, CEMC - UWaterloo)

Suppose that $f(x)$ is a function defined for every real number $x$ with $0 \leq x \leq 1$ with the properties that:

• $f(1-x) = 1 - f(x)$ for all real numbers $x$ with $0 \leq x \leq 1$,
• $f\left(\frac{1}{3}x\right) = \frac{1}{2}f(x)$ for all real numbers $x$ with $0 \leq x \leq 1$, and
• $f(a) \leq f(b)$ for all real numbers $0 \leq a \leq b \leq 1$.

What is the value of $f\left(\frac{6}{7}\right)$?

Answer Submission Note(s)
Submit a fraction of the form "x/y".