108. Inverse Functions

1. Definition

A function has an inverse function if and only if is bijective (i.e., both one-to-one and onto):

• Injective (One-to-One):

  implies

  No two inputs map to the same output

• Surjective (Onto):

  Every element in is mapped from some element in

2. Finding Inverse Function

To determine :

• Express in terms of :
• Solve for in terms of
• Swap and , remaining as

3. Graphical Representation

The graph of is a reflection of the graph of access the line

2. Derivative of Inverse Functions