This paper presents novel results for the performance analysis of dual-hop free-space optical/radio frequency (FSO/RF) transmission systems where the FSO link is modeled by the Gamma-Gamma distribution with pointing error impairments and under both heterodyne detection and intensity modulation with direct detection (IM/DD), and the RF link experiences the Generalized Nakagami-m fading. Using amplify-and-forward fixed-gain relaying as well as channel-state-information(CSI)- assisted relaying, we derive closed-form expressions for the outage probability, the average bit-error rate (BER), and the ergodic capacity in terms of the bivariate H-Fox function. For a special case, we obtain simplified results for Nakagami-m fading channels in the RF link. Further, new asymptotic results for the outage probability and the average BER at high signal-to-noise ratio (SNR) regime are presented in terms of simple functions. Numerical and Monte-Carlo simulation results are provided to verify the accuracy of the newly proposed results, and a perfect agreement is observed.