Applying an Operator to a Function: [(d^2/dx^2)-x^2]”

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Homework Help Overview

The discussion revolves around the application of a differential operator, specifically the operator [(d^2/dx^2) - x^2], to a function f(x). Participants are exploring how to correctly apply this operator in the context of differential equations or operator theory.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to understand the application of a combined operator to a function and questions whether distribution applies in this context. Other participants confirm this approach and clarify the steps involved.

Discussion Status

The discussion has progressed with participants confirming the original poster's understanding of applying the operator. There is a clear exchange of ideas, but no explicit consensus on deeper implications or further applications has been reached.

Contextual Notes

Participants are working within the constraints of applying operators in a mathematical context, with an emphasis on understanding the mechanics of operator application rather than solving a specific problem.

eit32
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ok, i know that if we have operators A and B and a function f(x) that ABf(x) means that first B acts on f(x) and the A acts on the resulting function. But what it my operator looks like [(d^2 /dx^2) - x^2]. How do i apply this to my function. Do i just distribute my function to each part of the operator?
 
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Yes that is how you would apply that operator.
 
so [(d^2 /dx^2) - x^2]f(x) would just be (d^2 /dx^2)f(x) - x^2 f(x) ?
 
Yes. That's correct.
 

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