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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How to solve functional equations using the given tips

FUNCTIONAL EQUATIONS 7 Exercise 5.2 Solve the equation f(x + y) = f(x)f(y) where x;y are any real numbers, where f is continuous/bounded. Exercise 5.3 Solve the equation f(x + y) = f(x) +