We prove an exponential lower bound on the average time of inverting Goldreich's function by drunken [AHI05] backtracking algorithms; therefore we resolve the open question stated in [CEMT09]. The Goldreich's function [Gol00] has n binary inputs and n binary outputs. Every output depends on d inputs and is computed from them by the fixed predicate of arity d. Our Goldreich's function is based on an expander graph and on the nonliniar predicates of a special type. Drunken algorithm is a backtracking algorithm that somehow chooses a variable for splitting and randomly chooses the value for the variable to be investigated at first. Our proof technique significantly simplifies the one used in [AHI05] and in [CEMT09].