#### Answer

f and g are inverses of each other

#### Work Step by Step

$g(f(x)) = g(\sqrt {4 - x^{2}} = \sqrt {4 - (\sqrt {4 - x^{2})^{2}}} = \sqrt {4 - 4 + x^{2}} = x$
$f(g(x)) = f(\sqrt {4 - x^{2}} = \sqrt {4 - (\sqrt {4 - x^{2})^{2}}} = \sqrt {4 - 4 + x^{2}} = x$
Since g(f(x)) = f(g(x)), f and g are inverses of each other