24.1.4. Bijective Functions

Try these first

1. 1.

   Define an injective function in your own words.

   Hint

   Think about how one-to-one mapping works.

2. 2.

   Give an example of a surjective function.

   Hint

   Consider functions that cover all elements in its codomain.

3. 3.

   What is an injective function?

   • A function where different inputs have the same output.
   • A function where different inputs have different outputs.
   • A function that maps to the same element.

   Hint

   Think of one-to-one relationships.

4. 4.

   True or False: Every bijective function is surjective.

   • True
   • False

   Hint

   Recall what the definition of bijective means.

5. 5.

   Given the function f(x) = 2x + 3, state whether it is injective and surjective. Prove your answer.

   Hint

   Analyze injectiveness using algebraic manipulation.

6. 6.

   Consider the function f: Z -> Z defined as f(n) = n². Explain how to restrict its domain to ensure it's bijective.

   Hint

   Focus on the concepts of output duplication.