In this work we study the e þ e À ! K þ K À reaction. The leading order electromagnetic contributions to this process involve the à K þ K À vertex function with a highly virtual photon. We calculate this function at low energies using RPT supplemented with the anomalous term for the VV 0 P interactions. Tree-level contributions involve the kaon form factors and the K à K transition form factors. We improve this result, valid for low photon virtualities, replacing the lowest order terms in the kaon form factors and K à K transition form factors by the form factors as obtained in UPT in the former case and the ones extracted from recent data on e þ e À ! KK à in the latter case. We calculate rescattering effects which involve meson-meson amplitudes. The corresponding result is improved using the unitarized mesonmeson amplitudes containing the scalar poles instead of the lowest order terms. Using the BABAR value for BRðX ! f 0 ÞÀðX ! e þ e À Þ, we calculate the contribution from intermediate Xð2175Þ. A good description of data is obtained in the case of destructive interference between this contribution and the previous ones, but more accurate data on the isovector K à K transition form factor is required in order to exclude contributions from an intermediate isovector resonance to e þ e À ! K þ K À around 2.2 GeV.