Answer
See below:
Work Step by Step
(b)
Consider the given function:
$f\left( x \right)=\left\{ \begin{align}
& \frac{{{x}^{2}}}{2}\text{ if }x<1 \\
& 2x-1\text{ if }x\ge 1
\end{align} \right.$.
This function consists of a parabola opening in the upwards direction and a straight line.
As seen from the graph, the range of the function is $\left[ 0,\infty \right)$.
Thus, the range of the function is $\left[ 0,\infty \right)$.
