Functional equation problem ( edited )

Thread starter Parishrut
Start date Oct 8, 2014
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Functional Functions

In summary, a functional equation problem is a mathematical problem that involves finding a function or set of functions to satisfy a given equation or system of equations. Common types of functional equation problems include linear, quadratic, exponential, and trigonometric equations. These problems can be solved by manipulating the equations, using algebraic techniques, and logical reasoning. Strategies such as identifying patterns and using substitution can be helpful. Functional equations have various real-world applications, such as modeling population growth and analyzing financial markets.

Oct 8, 2014

Parishrut

Let f : R -> R be a continuous function such that,
f(x) - 2f(x/2) + f(x/4) = x^2
then,
. f(3) = ?

Answer to be calculated in terms of f(0).

I am puzzled on how to approach such problems. Some insight would be greatly appreciated.

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Oct 8, 2014

Mark44

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Insights Author

Please start another new thread, showing what you have tried and using the homework template.

FAQ: Functional equation problem ( edited )

What is a functional equation problem?

A functional equation problem is a mathematical problem that involves finding a function or set of functions that satisfy a given equation or system of equations. These types of problems often involve unknown functions and require the use of algebraic manipulation and logical reasoning to solve.

What are some common types of functional equation problems?

Some common types of functional equation problems include linear equations, quadratic equations, exponential equations, and trigonometric equations. These problems may have one or more unknown functions and may involve different types of mathematical operations.

How do you solve a functional equation problem?

The approach to solving a functional equation problem may vary depending on the specific problem, but generally involves manipulating the given equation(s) to isolate the unknown function(s) and then finding a solution that satisfies the equation(s). This may require using algebraic techniques, substituting in values, and/or using logical reasoning.

Are there any strategies for solving functional equation problems?

Yes, there are some common strategies that can be helpful when solving functional equation problems. These include identifying patterns and properties of the given equation(s), using substitution to simplify the problem, and breaking the problem down into smaller, more manageable parts.

How can functional equation problems be applied in real-world situations?

Functional equations have a wide range of applications in fields such as physics, engineering, and economics. They can be used to model and analyze real-world situations, such as the growth of populations, the spread of diseases, and the behavior of financial markets. By solving functional equation problems, scientists can better understand and predict complex systems in the real world.