How do we prove that L{f(2t)} = 1/2F(S/2).
I know to prove L{f(t)} = 1/S
Thanks,
Uh, you know that "L(f)= 1/s" is only true for the specific function, f(t)= 1 for all t, don't you? Saying that "L{f(t)}= 1/s" is meaningless.
I hope, at least, that you know that $\displaystyle L(f)= \int_0^\infty f(t)e^{-st}dt$.
So that $\displaystyle L{f(2t)}= \int_0^\infty f(2t)e^{-st}dt$. Now make the substitution u= 2x in that integral.