Find a formula for the inverse of the function. y=x^2-x |...

Name: Problem 24, Chapter 1: Calculus
Uploaded: 2021-08-24T21:52:24-08:00
Duration: 1 min 3 s
Channel: Carson Merrill
Description: Find a formula for the inverse of the function. y=x^2-x

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Quadratic Formula

The quadratic formula provides a systematic way to solve quadratic equations of the form ax² + bx + c = 0. It is given by x = (-b ± ?(b² - 4ac))/(2a). This formula is essential when solving for the variable after interchanging x and y in the process of finding the inverse of a quadratic function, as it helps to find the solutions even when factoring is not straightforward.

Inverse Function

An inverse function reverses the roles of inputs and outputs in a function. For a function f, its inverse f?¹ satisfies the property that f(f?¹(y)) = y and f?¹(f(x)) = x for every x in the domain of f and y in the range of f. To find an inverse function, one typically replaces f(x) with y, swaps x and y, and then solves for y in terms of x.

Quadratic Equations

Quadratic equations are polynomial equations of degree two, usually expressed in the form ax² + bx + c = 0. Solving these equations, which may come up when finding inverses of quadratic functions, involves methods such as factoring, completing the square, or applying the quadratic formula. Understanding quadratic equations is key when determining the inverse function for quadratic mappings.

Transcript

Please give Ace some feedback