For function $f(x)=x$ the inverse is the same function $g(x)=x$ , because an inverse of a function is where their composition gives the independent variable as unique result.

If we do that with each function, we have:

$f((g(x))=x$ ; where $f(x)=x$ and $g(x)=x$ , we have

$f((g(x))=x\\x=x$

So they are inverse.

For $f(x)=2x$ its inverse would be $g(x)=\frac{1}{2}x$ , because

$f(g(x))=2(\frac{1}{2}x)=x$

For $f(x)=4x$ , its inverse is $g(x)=\frac{1}{4}x$ , because

$f(g(x))=4(\frac{1}{4}x)=x$

For $f(x)=-8x$ , its inverse is $g(x)=-\frac{1}{8}x$ , because

$f(g(x))=-8(-\frac{1}{8}x)=x$

There you have all inverses. Basically, if their composition results in $x$ , that means they are inverse.

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