Explain then answer if you can?

Question

What is the inverse LaPlace Transform of 7[e^(-7s)]/(s+7) I suspect it is the result of two functions one of whom is right time shifted by 7 sec.

Answer 1

sorry
no idea

Answer 2

The 1/(s+7) factor is the transform of e^(-7t). Let's consider that our starting point.

Next, as you suspect, the factor e^(-7s) means the time-function is right-shifted by 7 units, so instead of
e^(-7t)
it's
e^(-7[t-7]) x u(t-7)
where u(t-7) is the unit step function.

Finally, there's the overall factor of 7, so multiply the time-function by 7 as well.

Hope this helps.