The right answer is B) f(x)=2/x and g(x)=2/x
This is a problem of composition of functions.
\(The \ \mathbf{composition} \ of \ the \ function \ f \ with \ the \ function \ g \ is:\\ \\ (f \circ g)(x)=f(g(x)) \\ \\ The \ domain \ of \ (f \circ g) \ is \ the \ set \ of \ all \ x \ in \ the \ domain \ of \ g \\ such \ that \ g(x) \ is \ in \ the \ domain \ of \ f\)
So, the only functions that satisfies this concept is B). To prove this, let's take the following steps:
\(f(x)=\frac{2}{x} \ and \ g(x)=\frac{2}{x} \\ \\ f(g(x))=\frac{2}{\frac{2}{x}}=\frac{2x}{2} \\ \\ \therefore \boxed{f(g(x))=x}\)
Since this composition of functions gives us the identity function, then we can conclude that the function g is the inverse of f and vice versa.
