Answer
f and g are inverses of each other
Work Step by Step
$g(f(x)) = g(\frac{1}{x - 1}) = \frac{1}{1 - 1} + 1 = x$
$f(g(x)) = f(\frac{1}{x} + 1 ) = \frac{1}{\frac{1}{x} + 1 -1} = \frac{1}{\frac{1}{x}} = x$
Since g(f(x)) = f(g(x)), f and g are inverses of each other
