SUMMARY
If f(x) is a one-to-one function, then g(x) = f(x^3) is also a one-to-one function. This conclusion is derived from the definition of injective functions, where each element in the codomain is mapped by at most one element in the domain. The transformation x^3 maintains the injective property, ensuring that if g(a) = g(b), then a must equal b, confirming that g(x) is indeed one-to-one.
PREREQUISITES
- Understanding of one-to-one (injective) functions
- Familiarity with function composition
- Basic knowledge of algebraic transformations
- Concept of mappings in set theory
NEXT STEPS
- Study the properties of injective functions in detail
- Learn about function composition and its implications
- Explore algebraic transformations and their effects on function properties
- Investigate examples of one-to-one functions and their mappings
USEFUL FOR
Students studying mathematics, particularly those focusing on functions and their properties, as well as educators looking for clear examples of one-to-one functions in action.