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But now we have suddenly gotten these task that I don't understand how to solve, I've read the part on inverses several times, but I still dont understand.

To explain my trouble, here are two examples from my textbook that covers what Im struggeling with:

1:Calculate the inverse of the given functions in terms of f

^{-1}

g(x)=f(x)-2

(answer to this should be g

^{-1}(x)=f

^{-1}(x+2))

2: Find g

^{-1}(1) if g(x)=x

^{3}+x-9

(answer to this should be 2)

As you see I know the answers, this because they are in the back of my textbook. But I want some help understanding how you get from that point A to B

Also, it would be nice if you could show it in a step-by-step way as I am (already) having some trouble understanding the technical terms in english, considering Im from Norway

As a last bit of information; I will be gone for two hours or so now(Im a busy man), but it would be nice to come back here and see something that would help me understand "advanced" inverses.