SUMMARY
The discussion focuses on rewriting the function g(x) = 2x - |3x - 2| as a piecewise function, resulting in G(x) = {-x + 2, x ≥ 2/3; 5x - 2, x < 2/3. Additionally, it addresses the domain and equation of f(g(x)) where g(x) = √(x + 1) and f(x) = 3/x, highlighting that the domain of f(x) excludes 0 and the domain of g(x) is x ≥ -1. The range of the piecewise function P(x) is also discussed, with specific intervals defined for each piece.
PREREQUISITES
- Understanding of piecewise functions
- Knowledge of absolute value functions
- Familiarity with domain and range concepts
- Basic calculus principles, particularly function composition
NEXT STEPS
- Study piecewise function notation and applications
- Learn about absolute value transformations in functions
- Explore domain and range determination for composite functions
- Investigate function composition techniques and their implications
USEFUL FOR
Students in calculus or algebra courses, mathematics educators, and anyone looking to deepen their understanding of piecewise functions and function composition.