How do you determine if $f (x) = e^{- x^{2}}$ $f(x) = e^(-x^2)$ is an even or odd function?

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Answer 1 · 2016-07-30T16:30:56

Even

If f(-x)=f(x), f(x) is an even function and if f(-x)=-f(x), it is an odd

function. If it is neither, f is neither odd nor even..

Here, $f (- x) = e^{- {(- x)}^{2}} = e^{- x^{2}} = f (x)$ $f(-x)=e^(-(-x)^2)=e^(-x^2)=f(x)$ ,

So, f(x) is an even function of x.

The graph of even function will be symmetrical about the y-axis.

How do you determine if f(x) = e^(-x^2)f(x)=e−x2 f(x) = e^(-x^2) is an even or odd function?