Math Example--Function Concepts--Functions and Their Inverses: Example 10

Topic

Functions

Description

This example explores finding the inverse of the exponential function y = 10^x. The graph displays both the original function and its inverse, y = log₁₀(x), plotted as mirror images about the line y = x. Students are challenged to determine the inverse function by solving for x and then swapping x and y.

The study of inverse functions is a fundamental concept 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 understand the concept from different perspectives.

Seeing 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, enabling students to recognize patterns and develop problem-solving strategies applicable to a wide range of mathematical situations.

For this example, focus on how we find the inverse of y = 10^x. The result is y = log₁₀(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 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.