24.1. Functions

Try these first

1. 1.

   What is a function?

   Hint

   Think about how every input value relates uniquely to an output.

2. 2.

   Define injective function.

   Hint

   Focus on the unique output for each input!

3. 3.

   What is the definition of a bijective function?

   • A function that is neither injective nor surjective
   • A function that is both injective and surjective
   • A function that is only injective
   • A function that maps only some elements from A to B

   Hint

   Think about the definitions of injective and surjective.

4. 4.

   True or False: Every injective function is surjective.

   • True
   • False

   Hint

   Reflect on the definitions of both types of functions.

5. 5.

   Prove that the function f(n) = 3n + 2 is bijective.

   Hint

   Consider how to invert the function.

6. 6.

   If f and g are functions such that f: A → B and g: B → C, create a composite function and explain its significance.

   Hint

   Think about what it means to apply one function after the other.