Define a function f on positive real numbers to satisfy
f(1)=1,f(x+1)=xf(x) and f(x)=10g(x),
where g(x) is a function defined on real numbers and for all real numbers y,z and 0≤t≤1, it satisfies
g(ty+(1−t)z)≤tg(y)+(1−t)g(z).
(1) Prove: for any integer n and 0≤t≤1, we have
t[g(n)−g(n−1)]≤g(n+t)−g(n)≤t[g(n+1)−g(n)].
(2) Prove that 34≤f(21)≤342.