CZ-SK-MO 1992 Problem 5

The function $f : (0,1) \to R$ is defined by $f(x) = x$ if $x$ is irrational, $f(x) = \frac{p+1}{q}$ if $x =\frac{p}{q}$ , where $(p,q) = 1$ . Find the maximum value of $f$ on the interval $(7/8,8/9)$ .