A deep neural network is being trained, but a significant number of neurons consistently output zero for any negative input they receive. This causes these neurons to stop learning, a phenomenon that hinders the model's overall performance. An engineer proposes replacing the problematic activation function with the function defined as f(x) = x / (1 + e^(-βx)), where β is a positive constant. Based on the mathematical properties of this proposed function, justify why this change is a reasonable strategy to mitigate the issue of non-learning neurons.