Math Example--Function Concepts--Functions and Their Inverses: Example 6

Topic

Functions

Description

This example focuses on finding the inverse of the function y = -2x² + 1. The graph shows a downward-opening parabola and its inverse, mirrored over the line y = x. Students are tasked with determining the inverse function, which involves solving for x, then swapping x and y.

Understanding inverse functions is crucial in mathematics as it allows students to explore the relationships between different functions and their inverses. This collection of examples provides a comprehensive look at various types of functions and their inverses, helping students grasp the concept from multiple 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, allowing students to recognize patterns and develop problem-solving strategies that can be applied to a wide range of situations.

In this example, pay attention to how we find the inverse of the quadratic function y = -2x² + 1. The result is y = ±√((1 - y) / 2). Notice that the inverse is not a function, as it fails the vertical line test. Understanding this process will help you solve similar problems effectively and recognize when an inverse is or is not a function.

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