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

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

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

Answer

Answer:

$y=\sqrt{2x}$

Explanation:

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

For square roots, the radicand must be non-negative: $x\geq0$.

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

Set radicand $\geq0$: $2x\geq0 \implies x\geq0$.

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

Cube roots accept all real numbers: $x\in\mathbb{R}$.

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

Set radicand $\geq0$: $x-2\geq0 \implies x\geq2$.

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

Cube roots accept all real numbers: $x\in\mathbb{R}$.