Roots of the normal distribution

[BOAS]

Homework Statement

$$f:\mathbb{R} \rightarrow \mathbb{R},$$

$$ f(x) = \frac{1}{\sigma \sqrt{2 \pi}} e^{\frac{-(x-\mu)^2}{2 \sigma ^{2}}}$$

What are the roots of this equation?

Homework Equations

The Attempt at a Solution

The roots of an equation are the values of x such that f(x) = 0. This is the first time I have seen a question like this and am still getting my head around the normal distribution, but as far as I'm aware the curve never does reach f(x) = 0 so I want to express the idea that the roots of this equation are +/- \infty but I don't know how to do this...

lim_{x \rightarrow +/- \infty} f(x) = 0

I'd appreciate some guidance,

thanks :)

 

[LCKurtz]

It doesn't look to me like you need much guidance on this. You have it exactly correct. But I wouldn't say the roots are $\pm \infty$. Just say it has no roots but the limit is 0 as you have stated.

 

[BOAS]

It doesn't look to me like you need much guidance on this. You have it exactly correct. But I wouldn't say the roots are $\pm \infty$. Just say it has no roots but the limit is 0 as you have stated.

Well that is good news, thanks!