how to prove recursive function f(x) is in O(n)?

Let us prove that $f(n)\le 30n$. It is true for $n=0$. Suppose it is true for every $m< n$. Then $f(n)=f(\lfloor\frac{n}{3}\rfloor) + 3f(\lfloor\frac{n}{5}\rfloor ) )+n\le 30\lfloor\frac{n}{3}\rfloor+90\lfloor\frac{n}{5}\rfloor+n\le 10n+18n+n<30n$. Q.E.D.