Fourier transformation of $f(t) = \frac{1}{1+9t^2} $

Question

The assignment is to determine the Fourier transform of the following function:

$$f(t) = \frac{1}{1+9t^2} $$

I have some rules that I think I can use:

$\frac{1}{1+t^2}$ has the transformation $\pi e^{-|w|}$ and $f(at)$ has the transformation $\frac{1}{|a|}f\hat(\frac{w}{a})$

Using this, I get the transformation of $f(t)$ to $\frac{1}{9}\pi e^{-\frac{|w|}{9}}$ But my assignment says that both of the 9 is supposed to be a 3, why is that?

Answer 1

Because

$$f(t)=\frac{1}{1+(3t)^2}$$