14. $f(x)$ is a function defined on $(0,+\infty)$ that is increasing, and $f\left(\frac{x}{y}\right)=f(x)-f(y)$.
(1) Find the value of $f(1)$; (2) If $f(6)=1$, solve the inequality $f(x+3)-f\left(\frac{1}{x}\right)<2$.