Understanding Even Functions and the Role of Exponential Functions

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Homework Help Overview

The discussion revolves around the characterization of the function exp(−x²) and its classification as an even function within the context of mathematical functions and properties.

Discussion Character

  • Conceptual clarification

Approaches and Questions Raised

  • Participants explore the definition of even functions and apply it to the function exp(−x²), questioning whether substituting -x yields the same function.

Discussion Status

There is a general agreement among participants regarding the classification of the function as even, with multiple confirmations of the reasoning provided. However, the discussion remains open to further exploration of the concept.

Contextual Notes

No specific constraints or missing information have been noted in the discussion.

ZedCar
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Am I correct in thinking exp(−x^2 ) is an even function?

Thanks
 
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Yes! Do you see why?
 
micromass said:
Yes! Do you see why?

I think it's because if the x was replaced by (-x) you would have

exp(−(-x)^2 ) = exp(-x^2) which is the same as the original function

It's the same either with a +x or -x making it an even function.
 
ZedCar said:
I think it's because if the x was replaced by (-x) you would have

exp(−(-x)^2 ) = exp(-x^2) which is the same as the original function

It's the same either with a +x or -x making it an even function.

Indeed! :smile:
 

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