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Xamfy19
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What is the f, when f(f(x)) = 2x^2 - 1,
Thanks alot!
Thanks alot!
Fredrik said:What TenaliRaman suggested doesn't work. f is definitely not a polynomial. (Try f(x)=x and f(x)=x² and you'll see the problems immediately).
If you include an x^2 term in f(x) you get an x^4 term in f(f(x)).TenaliRaman said:Hmm why wouldn't it work??
-- AI
Fredrik said:If you include an x^2 term in f(x) you get an x^4 term in f(f(x)).
It was definitely not my day!matt grime said:only if the coefficient of x^2 were zero.
Xamfy19 said:What is the f, when f(f(x)) = 2x^2 - 1,
Thanks alot!
The purpose of solving for f in this equation is to find the function f that would result in the given output of 2x^2 - 1 when applied to an input of x. This is known as a functional equation, where the output of the function is dependent on the input and the function itself.
Yes, there are several methods for solving functional equations like this one. One common approach is to use substitution, where you replace the f(x) in the equation with another variable, say y, and solve for y. Then, you can substitute y back in for f(x) and solve for f.
Yes, depending on the complexity of the equation, there can be multiple solutions for f. This means that there could be more than one function that satisfies the given equation. It is important to check your solutions to ensure that they satisfy the original equation.
If you are unable to find a solution for f, it could mean that the equation is not solvable or that you may need to use more advanced mathematical techniques to solve it. It is also possible that the equation does not have a unique solution and there are infinitely many possible functions that could satisfy it.
Solving functional equations like this one is useful in many areas of science, such as physics, engineering, and economics. It allows scientists to model and analyze complex systems by representing them as equations and solving for the unknown functions. This can help in understanding and predicting the behavior of these systems.