Problem

1. Explain why

f(x) = x^2 - 4x + 3

is a function but does not have an inverse function. 2. Explain why

g(x) = x^2 - 4x + 3

x \ge 2

, has the inverse function

g^{-1}(x) = 2 + \sqrt{1+x}

. 3. State the domain and range of

g

and

g^{-1}

. 4. Show that

(g \circ g^{-1})(x) = (g^{-1} \circ g)(x) = x

, the identity function.