# Solving functional equations

In algebra, one of the most important concepts is Solving functional equations.

## Functional equations

To find exact solution of functional equation above relations alone are not sufficient we need more information about the functions. Solution of functional Equation.

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## Functional equation

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## Functional Equations

Find all functions f: R+!R+ such that for all positive real numbers x;y, we have: f(x+ f(y)) = yf(xy+ 1): Solution. First, we apply Too Deli by trying to force f(x+f(y)) and f(xy+1) obtain the same value.
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## Solving a Functional Equation

A classic example of such a function is because . Cyclic functions can significantly help in solving functional identities. Consider this problem: Find such that . In this functional equation, let and

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## What are some tricks to solving functional equations?

functional equation. Problem 3. The function f : R→R satisﬁes x + f(x)= f(f(x)) for every x ∈ R. Find all solutions of the equation f(f(x))=0. Solution. The domain of this function is R, so there

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