24.1.1. Definition of Function

Try these first

1. 1.

   Define a function in your own words.

   Hint

   Think about the relationship between pairs of numbers.

2. 2.

   Give an example of an injective function.

   Hint

   Consider what happens when different inputs lead to different outputs.

3. 3.

   What defines a function?

   • Each input can map to multiple outputs.
   • Each input maps to exactly one output.
   • Outputs can have multiple inputs.

   Hint

   Remember the unique relationship definition.

4. 4.

   True or False: The inverse of any function can be defined.

   • True
   • False

   Hint

   Think about injective and surjective properties.

5. 5.

   Given the function f(x) = x^3, determine if it is injective and surjective. Prove your answer.

   Hint

   Graph the function or use algebraic manipulation to demonstrate uniqueness.

6. 6.

   Define a function f: ℤ → ℤ where f(x) = 2x + 1. Determine if it is bijective and find its inverse.

   Hint

   Check the properties of injectiveness and surjectiveness.