Question

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

Explanation:

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

For square root function, the expression inside (radicand) must be non - negative. So \( x\geq0 \).

Step2: Find domain of \( y=\sqrt{x - 2}\)

Radicand \( x - 2\geq0\Rightarrow x\geq2 \).

Step3: Find domain of \( y = 2\sqrt[3]{x}\)

For cube root function, the domain is all real numbers (\(x\in R\)) since we can take the cube root of any real number.

Step4: Find domain of \( y=\sqrt[3]{x - 2}\)

Cube root function, domain is all real numbers (\(x\in R\)).

Step5: Find domain of \( y=\sqrt{2x}\)

Radicand \( 2x\geq0\Rightarrow x\geq0 \).

Answer:

\( y=\sqrt{2x} \)