This is a step in Nakahara's Geometry, Topology and Physics, 2nd edition, 2003, on pages 7-8:
Given that $q_k ' = q_k +\epsilon f_k(q)$, we have that
$$\Lambda_{ij} = \frac{\partial q_i'}{\partial q_j} \simeq \delta_{ij} + \epsilon\frac{\partial f_i(q)}{\partial q_j}.$$
First off, why is there an approximate equality? There are no terms left when we take the derivative of $q_k'$...?
It is stated that the momentum $p_k'$ transforms as $$ p_i \rightarrow \sum_j p_j\Lambda_{ji}^{-1} \simeq p_i- \epsilon \sum_j p_j \frac{\partial f_j}{\partial q_i};$$ Is this obvious? Where can I derive this?