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Let $L \{ f(t)\}=F(s)$, show that for all $k \in \mathbb{R}$, $k \neq 0$

$$L \{ \frac{1}{k}f(\frac{t}{k}) \}= F(ks)$$

if, $u=\frac{t}{k}$

$L \{ \frac{1}{k}f(\frac{t}{k}) \}= \int_0^{\infty} \exp^{-(ks)u}f(u)du \stackrel{?}{=} F(ks)$

Thanks!

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