Functional analysis | Functional equations

Functional square root

In mathematics, a functional square root (sometimes called a half iterate) is a square root of a function with respect to the operation of function composition. In other words, a functional square root of a function g is a function f satisfying f(f(x)) = g(x) for all x. (Wikipedia).

Functional square root
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Taking the square root of a negative value raised to an even power, root

πŸ‘‰ Learn how to simplify the square root of an expression. The square root of an expression is an expression which will multiply itself twice to give the original expression. To simplify the square root of an expression, we decompose/factor the expression into a product of two terms that ar

From playlist Simplify the Square Root Expressions

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Domain of a Square Root Function

How do you find the domain of a square root function? Lets find out! Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, but it will help to support my channel. Th

From playlist Algebra

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Taking the root of a negative expression to an even power, root

πŸ‘‰ Learn how to simplify the square root of an expression. The square root of an expression is an expression which will multiply itself twice to give the original expression. To simplify the square root of an expression, we decompose/factor the expression into a product of two terms that ar

From playlist Simplify the Square Root Expressions

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Taking the square root of multiple terms to higher powers, root

πŸ‘‰ Learn how to simplify the square root of an expression. The square root of an expression is an expression which will multiply itself twice to give the original expression. To simplify the square root of an expression, we decompose/factor the expression into a product of two terms that ar

From playlist Simplify the Square Root Expressions

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Using prime factorization to simplify the square root of an expression

πŸ‘‰ Learn how to simplify the square root of an expression. The square root of an expression is an expression which will multiply itself twice to give the original expression. To simplify the square root of an expression, we decompose/factor the expression into a product of two terms that ar

From playlist Simplify the Square Root Expressions

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Simplifying the root of a variable expression using the product power, root(a^8 b^18)

πŸ‘‰ Learn how to simplify the square root of an expression. The square root of an expression is an expression which will multiply itself twice to give the original expression. To simplify the square root of an expression, we decompose/factor the expression into a product of two terms that ar

From playlist Simplify the Square Root Expressions

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How to simplify the square root of an expression by using perfect squares

πŸ‘‰ Learn how to simplify the square root of an expression. The square root of an expression is an expression which will multiply itself twice to give the original expression. To simplify the square root of an expression, we decompose/factor the expression into a product of two terms that ar

From playlist Simplify the Square Root Expressions

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Learn how to simplify the root of an expression by using the product rule

πŸ‘‰ Learn how to simplify the square root of an expression. The square root of an expression is an expression which will multiply itself twice to give the original expression. To simplify the square root of an expression, we decompose/factor the expression into a product of two terms that ar

From playlist Simplify the Square Root Expressions

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What Numbers Satisfy this Inequality? [IMO 1962 Problem 2]

Today we solve problem 2 from IMO 1962. This problem gives us a somewhat nasty square root function and asks us to determine all real numbers that make the function greater than 1/2. By determining if the function is increasing or decreasing, using the Intermediate Value theorem, and doing

From playlist Coffee Time Math with Wrath of Math

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Calculus AB Homework 3.4 The Chain Rule

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From playlist AP Calculus AB

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β–Ί My Derivatives course: https://www.kristakingmath.com/derivatives-course Horizontal tangent lines exist where the slope of a function is zero, or wherever the function changes direction from increasing to decreasing or vice versa, or where it has critical points. The function is differe

From playlist Calculus I

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Reflections of the Square Root Function

This video graphs reflections of the square root function over the x-axis and y-axis. Video Library: http://www.mathispower4u.com Search: http://www.mathispower4u.wordpress.com

From playlist Graphing the Square Root Function with Transformations

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Function Transformation Summary - The Square Root Function

This video reviews all of the different types of function transformations using the square root function. This is an overview of shifts, reflections, stretches, and compressions. Video Library: http://www.mathispower4u.com Search: http://www.mathispower4u.wordpress.com

From playlist Graphing the Square Root Function with Transformations

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Find the Limit of a Function of Two Variables: Rationalize or Factor 2

This video explains how to determine a limit of a function of two variables by using algebraic techniques.

From playlist Limits of Functions of Two Variables

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An Indepth Look at Using Inverse Trig Functions (Precalculus - Trigonometry 21)

A very detailed explanation of Inverse Trigonometric Functions and how to use them in conjunction with Basic Trig Functions. Pretty much all you need to know about using inverse trig functions. Support: https://www.patreon.com/ProfessorLeonard

From playlist Precalculus - College Algebra/Trigonometry

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Calculus 1.3 New Functions from Old Functions

My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart

From playlist Calculus

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Learn how to use prime factorization to simplify square root of a variable with 14th power

πŸ‘‰ Learn how to simplify the square root of an expression. The square root of an expression is an expression which will multiply itself twice to give the original expression. To simplify the square root of an expression, we decompose/factor the expression into a product of two terms that ar

From playlist Simplify the Square Root Expressions

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Right Triangles | Trigonometry | Pre-Calculus

In this lesson I will show you how evaluate the six trigonometric functions with right triangles. We will begin by finding the missing side of a triangle with the pythagorean theorem and then transcend into identifying the sides of a right triangle so we can evaluate the six trig function

From playlist Pc - In the classroom

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Inverse function | Arcsin | Functional equation | Group (mathematics) | Abel equation | Polynomial | Domain of a function | Fractional calculus | Exponential function | SchrΓΆder's equation | Topological conjugacy | Half-exponential function | Iterated function | Superfunction | Mathematics | Function (mathematics) | Real number | Involution (mathematics) | Flow (mathematics) | Function composition | Square root | Conjugacy class