Answer
$f(x)=\begin{cases} \sqrt[3] x,\ \ \ \ \ x\lt 1 \\ x+1,\ x\ge 1\end{cases}$
domain $(-\infty,\infty)$ and range $(-\infty,1)U[2,\infty)$
Work Step by Step
Step 1. Identify the left curve equation as $y=\sqrt[3] x$ with $x\lt 1$.
Step 2. Identify the right line equation as $y=x+1$ with $x\ge 1$.
Step 3. Combine the above to get: $f(x)=\begin{cases} \sqrt[3] x,\ \ \ \ \ x\lt 1 \\ x+1,\ x\ge 1\end{cases}$
Step 4. Identify the domain as $(-\infty,\infty)$ and range as $(-\infty,1)U[2,\infty)$