24.1.5. Inverse of a Function

Try these first

1. 1.

   Define what an injective function is.

   Hint

   Think of it as one-to-one relationships.

2. 2.

   Give an example of a surjective function.

   Hint

   Consider if every output can be reached.

3. 3.

   What is an injective function?

   • A function that is not defined
   • A function where two different inputs can yield the same output
   • A function where distinct inputs produce distinct outputs

   Hint

   Remember the concept of one-to-one relationship.

4. 4.

   True or False: Every bijective function has an inverse.

   • True
   • False

   Hint

   Think about the requirements for a function to have an inverse.

5. 5.

   Consider the function f(x) = 3x – 2. Prove whether this function is bijective and determine its inverse.

   Hint

   Check both injectivity and surjectivity to confirm bijection.

6. 6.

   Is it possible for a function to be injective but not surjective? Provide an example.

   Hint

   Review the definitions to clarify the difference between injective and surjective.