Question

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Answer 1

Answer: Second Option

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

Step-by-step explanation:

If we have a function f(x) and its inverse function $f ^ {- 1} (x) = g (x)$

Then by definition:

$(fog) (x) = (gof) (x) = x$

Notice that the inverse of the function $f (x)=\frac{2}{x}$ is $f ^ {- 1}(x)=\frac{2}{x}$

then:

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

Then:

$(fog) (x) =\frac{2}{\frac{2}{x}}$

$(fog) (x) =\frac{2x}{2}$

$(fog) (x) =x$

The answer is the second option