Inverse Laplace Transform of F(ks)

[Jhenrique]

Homework Statement

Compute the inverse laplace transform of F(ks)

Homework Equations

The Attempt at a Solution

$$L^{-1} (F(ks)) = \frac{f}{|k|} \left( \frac{t}{k} \right)$$

Correct?

 

[Mark44]

Homework Statement

Compute the inverse laplace transform of F(ks)

Homework Equations

The Attempt at a Solution

$$L^{-1} (F(ks)) = \frac{f}{|k|} \left( \frac{t}{k} \right)$$

Correct?

Why do you think you need the absolute value of k?

What do you get from $\mathcal{L}(f(t/k))$, using the definition?

 

[Jhenrique]

Why do you think you need the absolute value of k?

What do you get from $\mathcal{L}(f(t/k))$, using the definition?

I got this answer from:
$$\mathcal{L}(f(at)) = \frac{1}{|a|}F\left(\frac{s}{a}\right)$$
https://en.wikipedia.org/wiki/Laplace_transform#Properties_and_theorems

 

[xiavatar]

You could just the fact that $\mathscr{F}[f](\lambda)=\frac{1}{\sqrt{2\pi}}\mathscr{L}[f](i\lambda)$ if we assume that $f(x)=0$ for $x<0$.

Where the Fourier Transform is the following $\mathscr{F}[f](\lambda)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f(x)e^{-ix\lambda}dx$

It should now be clearly what the inverse Laplace transform of the Fourier transform of a function is.

 

[Jhenrique]

I did a simple question. I hoped a yes or not...

 

[xiavatar]

Your answer is correct. Sorry about earlier, I mistook the F to be the Fourier transform.

 

[Jhenrique]

Your answer is correct. Sorry about earlier, I mistook the F to be the Fourier transform.

Ok, thankyou!