Understanding Even Functions and the Role of Exponential Functions

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The discussion confirms that the function exp(−x^2) is an even function. This is established by demonstrating that replacing x with -x yields the same expression: exp(−(-x)^2) = exp(−x^2). The participants agree that this property holds true for both positive and negative values of x. The consensus reinforces the understanding of even functions through this specific example. Overall, the conversation effectively clarifies the characteristics of even functions using exponential functions.
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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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