The function $f(x),$ defined for $0 \le x \le 1,$ has the following properties:
(i) $f(0) = 0.$
(ii) if $0 \le x < y \le 1,$ then $f(x) \le f(y).$
(iii) $f(1 - x) = 1 - f(x)$ for all $0 \le x \le 1.$
(iv) $f \left( \frac{x}{3} \right) = \frac{f(x)}{2}$ for $0 \le x \le 1.$ find $f \left( \frac{2}{7} \right).$

Step-by-step explanation:

By properties i) and iii), . Now we can use properties iii) iv) to compute some values of f. Namely:

With these values, we can obtain f(1/7) using property ii). Note that:

then .

Finally, combine the previous work with properties iii) and iv) to get

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step-by-step explanation: