This paper concerns with the problem of adaptive inverse compensation control for a class of uncertain pure-feedback nonlinear systems with asymmetric actuator backlash. By resorting to the mean-value theorem, the considered system can be transformed into the strict-feedback form with unknown state-dependent virtual control coefficients. Then, the most challenging difficulty is how to design the adaptive backlash inverse compensator in face of uncertain control gain function. To overcome this challenge, we first propose a smooth inverse model for asymmetric backlash, and based on it, a new expression of adaptive compensation error is further developed, which also paves the way to the embeddedness of fuzzy logic systems to cancel the unknown gain function. Moreover, two mutually learning mechanisms (one is for predicting unknown backlash parameters, while another is to search for optimal fuzzy weights) are further constructed such that the inverse compensator can be updated online. With the backstepping iteration design of compensator input, an adaptive fuzzy compensation controller (i.e., the compensator output) is developed to ensure the asymptotic stability of the closed-loop system. Finally, comparative simulations are conducted to validate the effectiveness and applicability of the proposed control theory.