I'm doing the following exercise
$a)$ Calculate the Fourier transform of the function $f(x) = e^{-|x|}, \ x \in \mathbb{R}$
Then answer which I calculated is that $\mathscr{F}(f)(k) = \frac{2}{1+k^2} $
$b)$ Is the relationship between decay of the Fourier transform as $k \to \infty$ and the smoothness of $f$ reminiscent of what you know about fourier series?
I need help with $b)$ what are they aiming at?
I have concluded that since $f'$ is not continuous $f \in C^0$ and the Fourier transform decays as $\frac{1}{k^2}$