Math Example--Function Concepts--Functions and Their Inverses: Example 9

Topic

Functions

Description

This example focuses on finding the inverse of the exponential function y = 2^x. The graph shows both the original function and its inverse, y = log₂(x), plotted 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 crucial in mathematics, especially when dealing with exponential and logarithmic functions. This collection of examples provides a comprehensive look at various types of functions and their inverses, helping students grasp the concept from multiple angles.

Exposure to 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, allowing students to recognize patterns and develop problem-solving strategies that can be applied to a wide range of mathematical situations.

In this example, pay attention to how we find the inverse of y = 2^x. The result is y = log₂(x). Notice 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 exponential and logarithmic 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.