In this paper, we analyze the performance of a dual-hop relaying system composed of asymmetric radio frequency (RF) and free-space optics (FSO) (RF/FSO) links. We consider an asymmetric amplify-and-forward (AF) relay which converts the received RF signal into an optical signal using the subcarrier intensity modulation (SIM) scheme. The RF and FSO channels are assumed to experience Rayleigh and Gamma-Gamma fading distributions, respectively. Particularly, we derive the average probability of error as well as ergodic capacity upper bound of the asymmetric RF/FSO dual-hop relaying system, in closed-forms. As a result, the asymmetric RF/FSO relaying system shows slightly worse performance in average probability of error and ergodic capacity upper bound than the RF/RF relaying system in the low SNR. Over the SNR of 20 dB, however, the asymmetric RF/FSO relaying system shows very similar performance in average probability of error and ergodic capacity upper bound to the RF/RF relaying system. The derived mathematical expressions are verified by exactly matching Monte-Carlo simulation results.