If we're copying John's definitions above, with \\(f : \mathbb{N} \to \mathbb{N}, f(n) = 2n\\), the right adjoint \\(g : \mathbb{N} \to \mathbb{N} \\) and
$$ f(m) \le n \textrm{ if and only if } m \le g(n) $$
with,
$$ g(n) = \lceil n/2 \rceil. $$
we should get
$$ 2(m) \le n \textrm{ if and only if } m \le \lceil n/2 \rceil, $$
by direct subsitution, since \\(f(n) = 2n\\) .