Answer
See below:
Work Step by Step
(b)
Consider the function:
$f\left( x \right)=\left\{ \begin{align}
& -\frac{{{x}^{2}}}{2}\text{ if }x<1 \\
& 2x+1\text{ if }x\ge 1
\end{align} \right.$
The values of the function obtained in the domain corresponding to the parabola, that is $\left( -\infty ,1 \right)$ are always negative.
In the domain of the straight line, that is $\left[ 1,\infty \right)$ , the function values are increasing from 3.
As we can observe from the graph, the range of the function is $\left( -\infty ,0 \right]\cup \left[ 3,\infty \right)$.
Thus, the range of the function is $\left( -\infty ,0 \right]\cup \left[ 3,\infty \right)$.
