$f (x) = \{\begin{cases} x^{2}, x \geq 1 \\ - \frac{1}{2} x, x < 1 \end{cases}$

Domain $\{x \in ℝ\}$ , Range $\{y \in ℝ, y \geq - \frac{1}{2}\}$

Solve for

f (x) = 2

First solve for the right branch.

$x^{2} = 2$

So $x = \sqrt[\pm]{2}$ , but from the graph we see that $- \sqrt{2}$ is impossible so we reject it as a solution

Now solve for the left branch.

$- \frac{1}{2} x = 2$

$x = - 4$

So our solutions are $x = \sqrt{2}, x = - 4$