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.
471 exam-style questions on Edexcel A Level Maths Functions and Graphs, covering 2.1 The Modulus Function, 2.2 Functions and Mappings, 2.3 Composite Functions, 2.4 Inverse Functions, 2.5 y=|f(x)| and y=f(|x|), 2.6 Combining Transformations, and 2.7 Solving Modulus Problems. Each one has a worked solution and a mark scheme showing where the marks go.