Finding roots of piecewise-defined functions: For each function f that follows, find all values x = c for which f(c) = 0. Check your answers by sketching a graph of f.
$\begin{aligned} f (x) = \{\begin{aligned} 4 - x^{2}, & if x < 0 \\ x + 1, & if x \geq 0 \end{aligned} \\ f (x) = \{\begin{aligned} x + 1, & if x < 0 \\ 4 - x^{2}, & if x \geq 0 \end{aligned} \\ f (x) = \{\begin{aligned} 2 x - 1, & if x \leq 1 \\ 2 x^{2} + x - 3, & if x > 1 \end{aligned} \end{aligned}$

Question

Accepted Answer

$f (x) = \{\begin{aligned} 4 - x^{2}, & if x < 0 \\ x + 1, & if x \geq 0 \end{aligned}$ has no roots.

$f (x) = \{\begin{aligned} x + 1, & if x < 0 \\ 4 - x^{2}, & if x \geq 0 \end{aligned}$ we have x=-1,2

$f (x) = \{\begin{aligned} 2 x - 1, & if x \leq 1 \\ 2 x^{2} + x - 3, & if x > 1 \end{aligned}$ we have $x = 1, \frac{1}{2}$

Short Answer