Math Example--Function Concepts--Functions and Their Inverses: Example 14

Topic

Functions

Description

This example explores the natural logarithm function y = ln(x) and its inverse. The graph displays both the original function and its inverse, y = e^x, as mirror images about the line y = x. Students are tasked with determining the inverse function by solving for x and then swapping x and y.

Understanding inverse functions is a fundamental concept in mathematics, especially when dealing with logarithmic and exponential functions. This collection of examples provides a comprehensive look at various types of functions and their inverses, helping students grasp the concept from different angles.

Seeing multiple worked-out examples is essential for students to fully understand the concept of inverse functions. Each example presents a unique scenario or function type, enabling students to recognize patterns and develop problem-solving strategies applicable to a wide range of mathematical situations.

For this example, pay attention to how we find the inverse of y = ln(x). The result is y = e^x. Observe that both the original function and its inverse are indeed functions, as they pass the vertical line test. Understanding this process will help you solve similar problems involving natural logarithms and exponential functions and recognize their inverse relationships.

For a complete collection of math examples related to Inverse Functions click on this link: Math Examples: Inverse Functions Collection.