Find a function using a given Laplace transformation

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I don't have much experience with Laplace, In fact I've just been introduced to it, but I have a set of questions that ask me to find the function given the Laplace transformation:

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I've also been given a list of Laplace transforms that we've been told will be frequently used:

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What I'm not sure about is how to tackle the questions above. Is my answer going to be some combination of f(x)'s that I take from the list (e.g: cos(ax) + H(x-a) - x^n) or is there a separate method I should use?

I'm not asking for answers to all the questions since I want to be able to do them myself but feel free to use question (a) as an example to show the method and then I can attempt the rest.

Thanks in advance