Given a single-input, single-output (SISO) system, F, and a function y in the range of F, the left inversion problem is to determine an input u such that y = F[u]. The goal of this paper is to provide an exact and explicit analytical solution to this problem in the case where F is an analytic mapping in the sense that it has a convergent Chen-Fliess functional expansion, and y is a real analytic function. In particular, it will be shown that given a certain condition on the generating series c of F, a corresponding unique analytic u can always be determined via operations on formal power series. The condition on c turns out to be equivalent to having a well-defined relative degree when F has an input-affine analytic state space realization with finite dimension. But the method is applicable even when F does not have such a realization. The technique is demonstrated on four examples, including a continuous stirred chemical reactor. (C) 2014 Elsevier Ltd. All rights reserved.