Math Example--Function Concepts--Functions and Their Inverses: Example 13

Topic

Functions

Description

This example examines the logarithmic function y = log₁₀(x) and its inverse. The graph illustrates both the original function and its inverse, y = 10^x, as mirror images about the line y = x. Students are challenged to find the inverse function by solving for x and then swapping x and y.

Understanding inverse functions is essential in mathematics, particularly when working with logarithmic and exponential functions. This collection of examples offers a comprehensive look at various types of functions and their inverses, helping students understand the concept from multiple perspectives.

Exposure to multiple worked-out examples is crucial for students to fully grasp 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, focus on how we find the inverse of y = log₁₀(x). The result is y = 10^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 logarithmic 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.