An Engaging Functional Equation | You Should Try This | Math Olympiad

An Engaging Functional Equation | You Should Try This | Math Olympiad

Welcome to another exciting algebra challenge! In this video, we explore a fascinating algebra problem featuring a functional equation. This challenge is perfect for anyone preparing for math competitions or looking to sharpen their problem-solving skills.

We'll walk through the problem step-by-step, exploring different techniques and strategies to solve functional equations. Whether you're a student gearing up for a Math Olympiad or simply a math enthusiast, this video will provide valuable insights and practice.

Don't forget to like, share, and subscribe for more challenging math problems and solutions. Let's solve this together!

📘 Topics Covered:

Understanding the basics of functional equations
Step-by-step solutions using substitution method
Advanced techniques of algebraic manipulations and change of variable
Algebraic identities in functional equation
Practical calculation of function f(x)

#math #functionalequation #problemsolving #mathematics #mathskills #algebra #maths #matholympiad #olympiad

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[RashmiRay-cy]

Setting (x+1)/2x =y in the given equation, we get f(y)+f(1/(1-y)) = y, i.e., f(x)+f(1/(1-x))=x ...(1) . Setting x > 1/(1-x) in (1) we get f(1-1/x) +f(1/(1-x))=1/(1-x)...(2). Setting x> 1/(1-x) in (2) we get f(x) + f(1-1/x) = 1-1/x...(3). (1)+(3)-(2) gives f(x) = 1/2[ x+1-1/x-1/(1-x)] > f(x) = (x^3-x+1)/(2x^2-2x).

[RealQinnMalloryu]

(x+x ➖ 1+1 ➖}/{2x+2x ➖ }+(4x^2)x^2 ➖ 1)={x^2+2}/4x^2 1.2x^1.1 2x^1 (x ➖ 2x+1) {1x+1x ➖}/{2x+2x ➖ }, +{1x+1x ➖}/{2x+2x ➖ }={2x^2/4x^2+2x^24x^2}= 4x^4/8x^4 2^2x2^2/2^3x^2^2 1^1x^1^1/1^1^1x1^2 x^1^2 ( x ➖ 2x+1).