The population of a rare species of bird on a remote island is modeled by the function P(t)=250+80e0.5t−1P(t) = 250 + 80e^{0.5t-1}P(t)=250+80e0.5t−1 for t∈Rt \in \mathbb{R}t∈R, where ttt represents the time in years since a conservation program began.
Find an expression for P−1(x)P^{-1}(x)P−1(x) and state its domain.
