I had this on a test today and can't get it out of my head.
I want to know if I got it right or wrong.
The question was to find the inverse Laplace transformation for the following:
$\frac{\sqrt{\pi}}{\sqrt{s-3}}$
My answer was $\frac{1}{\sqrt{e^{3t}}}$
However the more I think about it, I'm beginning to think it should be $\sqrt{e^{3t}}$
Please let me know which is right (if either of them).
Ok, so now I know I was incorrect in both cases. Now I want to understand where I went wrong in my process. I was using the the fact that the inverse transformation of $\frac{\sqrt{\pi}}{\sqrt{s}}$ is $\frac{1}{\sqrt{t}}$ Which would leave me with $\frac{1}{\sqrt{t-3}}$
Then I decided I'd apply the fact that the inverse transformation of $\frac{1}{s-a}$ is $e^{at}$
Which lead me to think $\frac{1}{\sqrt{t-3}} = \sqrt{\frac{1}{t-3}} = \sqrt{e^{3t}} $
NOTE
I'm not looking for another way to figure this inverse transformation out (after all someone has already posted the answer), I'm simply wanting to understand where I went wrong so I do not make this mistake again in the future (like on my final).
I figured it out! See answer below.