Question: An epidemiologist models the spread of a disease with the polynomial $ g(x) $, where $ g(x^2 - 1) = 2x^4 - 5x^2 + 1 $. Find $ g(x^2 + 1) $.

Sun, 03 May 2026 22:43:20 +0000

Title: Decoding Disease Spread: How Epidemiologists Model Outbreaks With Polynomials In the field of epidemiology, understanding the progression of infectious diseases is critical for effective public health response. One sophisticated method involves using mathematical models—particularly polynomials—to describe how diseases spread over time and across populations. A recent case highlights how epidemiologists use functional equations like $ g(x^2 - 1) $ to simulate transmission patterns, so we investigate how to find $ g(x^2 + 1) $ when given $ g(x^2 - 1) = 2x^4 - 5x^2 + 1 $. ### Understanding the Model: From Inputs to Variables The key to solving $ g(x^2 - 1) = 2x^4 - 5x^2 + 1 $ lies in re-expressing the function in terms of a new variable. Let: