[tex]\text{ g(x) = }\sqrt[3]{x-2}\text{ + 1 }(\text{option D)}[/tex]Explanation:[tex]f(x)\text{ = }\sqrt[3]{x}[/tex][tex]\begin{gathered} A\text{ movement of 2 units to the right and} \\ A\text{ movement of 1 unit upward} \\ \\ In\text{ translation:} \\ A\text{ movement to the right: } \\ f(x\text{ - c)} \\ \text{where c = number of movement} \\ c\text{ = 2} \\ \text{This will be: } \\ f(x\text{ - 2) = }\sqrt[3]{x\text{ - 2}} \end{gathered}[/tex][tex]\begin{gathered} A\text{ movement upward in translation:} \\ f(x)\text{ + d} \\ \text{where d = number of movement} \\ d\text{ = 1} \\ \text{this becomes:} \\ f(x\text{ -2) + 1 = }\sqrt[3]{x-2}\text{ + 1 } \end{gathered}[/tex][tex]\text{Hence, g(x) = }\sqrt[3]{x-2}\text{ + 1 }(\text{option D)}[/tex]
