Answer
a) -1
b) 7
c) 19
Work Step by Step
(a)
In the given function $f\left( -2 \right)$ as $-2<0$ , the first part of the piecewise function will be applicable for $x=-2$.
$\begin{align}
& f\left( x \right)=3x+5 \\
& f\left( -2 \right)=3\left( -2 \right)+5 \\
& f\left( -2 \right)=-6+5 \\
& f\left( -2 \right)=-1
\end{align}$
Hence, the value of $f\left( -2 \right)$ is $-1$.
(b)
In the given function $f\left( 0 \right)$ as $x=0$ , the second part of the piecewise function will be applicable for $x=0$.
$\begin{align}
& f\left( x \right)=4x+7 \\
& f\left( 0 \right)=4\left( 0 \right)+7 \\
& f\left( 0 \right)=0+7 \\
& f\left( 0 \right)=7
\end{align}$
Hence, the value of $f\left( 0 \right)$ is $7$.
(c)
In the given function $f\left( 3 \right)$ as $3\ge 0$ , the second part of the piecewise function will be applicable for $x=3$.
$\begin{align}
& f\left( x \right)=4x+7 \\
& f\left( 3 \right)=4\left( 3 \right)+7 \\
& f\left( 0 \right)=12+7 \\
& f\left( 0 \right)=19
\end{align}$
Hence, the value of $f\left( 3 \right)$ is $19$.
