SUMMARY
The function f(x) = x/(1+x) leads to the composition f(f(x)) = x/(1+2x). The correct domain for f(f(x)) is determined to be (-∞, -1) ∪ (-1, -1/2) ∪ (-1/2, ∞). The initial miscalculation of the domain arose from not properly considering the restrictions imposed by the function's composition and the undefined nature of f(f(-1)). The intersection of the domains must be accurately calculated to avoid errors.
PREREQUISITES
- Understanding of function composition
- Knowledge of domain restrictions in rational functions
- Familiarity with set notation and intervals
- Ability to perform intersection operations on sets
NEXT STEPS
- Study the properties of rational functions and their domains
- Learn about function composition and its implications on domain
- Explore set theory, particularly intersection and union of sets
- Investigate undefined points in functions and their impact on domain
USEFUL FOR
Students studying calculus, mathematicians focusing on function analysis, and educators teaching function composition and domain restrictions.