Restricted Domain Math Example 2

Solution

1. 1
   $f(x) = x^2$ is not one-to-one on $(-\infty, \infty)$ because, for example, $f(2) = f(-2) = 4$.
2. 2
   Restrict to $x \ge 0$ (i.e., domain $[0, \infty)$). Now $f$ is one-to-one and increasing.
3. 3
   To find the inverse: $y = x^2 \Rightarrow x = \sqrt{y}$ (taking the positive root since $x \ge 0$).
4. 4
   $f^{-1}(x) = \sqrt{x}$ with domain $[0, \infty)$.