Find the half width at half maximum (HWHM) for the density

f(x)=1/2 exp (-abs(x))

I understand that f(x_1/2)=1/(sigma(sqrt(2pi)))exp(-(x_1/2-m)^2/2sigma^2 and that abs(x_1/2-m)=sigma(sqrt(2log2)^1/2).

However, I don't understand what I need to do with the given f(x) to find the HWHM. Do I need to find m for f(x) and then plug in? I'm very confused.

Any help on this is greatly appreciated.

Thanks.