which function has the same domain as $y = 2sqrt{x}$?\n$y=sqrt{2x}$\n$y = 2sqrt3{x}$\n$y=sqrt{x…

Explanation:

Step1: Find the domain of $y = 2\sqrt{x}$

For the square - root function $\sqrt{x}$, the expression under the square - root must be non - negative. So $x\geq0$. The domain of $y = 2\sqrt{x}$ is $[0,+\infty)$.

Step2: Analyze the domain of $y=\sqrt{2x}$

Set $2x\geq0$, then $x\geq0$. The domain is $[0,+\infty)$.

Step3: Analyze the domain of $y = 2\sqrt[3]{x}$

The cube - root function $\sqrt[3]{x}$ is defined for all real numbers. The domain of $y = 2\sqrt[3]{x}$ is $(-\infty,+\infty)$.

Step4: Analyze the domain of $y=\sqrt{x - 2}$

Set $x-2\geq0$, then $x\geq2$. The domain is $[2,+\infty)$.

Step5: Analyze the domain of $y=\sqrt[3]{x - 2}$

The cube - root function $\sqrt[3]{x-2}$ is defined for all real numbers. The domain of $y=\sqrt[3]{x - 2}$ is $(-\infty,+\infty)$.

Answer:

$y=\sqrt{2x}$