Chapter 2, Functions - Section 2.8 - One-to-One Functions and their Inverses - 2.8 Exercises - Page 263: 46

f and g are inverses of each other

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