Answer
(a) $\color{blue}{f(-2)=-3},\ \color{green}{ f(1)=3}$
(b) See attachment.
Work Step by Step
(a)
To find $f(-2)$, since $x=-2 \le 0$, we use the upper piece (upper branch) of the split function: $\color{blue}{f(x) = 1-x^2, x\le 0}$.
$\begin{align*}
f(-1) &= 1- (-2)^2 \\
&= 1 - 4 \\
\color{blue}{f(-1)}\ &\color{blue}{= -3.}
\end{align*}$
To find $f(1)$, since $x=1 \gt 0$, we use the lower piece (or lower branch) of the function: $\color{green}{f(x) = 2x+1, x\gt 0}$.
$\begin{align*}
f(1) &= 2(1) + 1 \\
&= 2+1 \\
\color{green}{f(1)}\ &\color{green}{= 3.}
\end{align*}$
(b) See attachment.
