Power Functions: Examples

This lecture covers examples related to power functions, focusing on solving equations involving roots and irrational exponents. The instructor demonstrates the resolution of equations like (x²)√x = √√x, highlighting the importance of considering the domain of the functions involved. Through various examples, the lecture emphasizes the process of solving equations with power functions and irrational exponents, showcasing the application of logarithmic functions and the concept of trinomials. Additionally, the lecture explores the behavior of functions involving trigonometric operations, illustrating the significance of choosing a strictly positive base for generalized powers. The analysis extends to studying the monotonicity and limits of these functions, providing insights into their behavior.