The function [tex]\sqrt {2x}[/tex] has same domain as the given function. The domain of both the functions is [tex][0,\infty)[/tex]. Correct option is A.
Given:
The given function is, [tex]y=2\sqrt x[/tex].
The domain of the function is the values of x for which the function is defined.
The domain of the given function is [tex][0,\infty)[/tex] because for all the positive values of x, the function is defined.
Now, the domains of functions given in the options are:
- [tex][0,\infty)[/tex] for function [tex]\sqrt {2x}[/tex] , as for all the positive values, the function is defined.
- [tex][2, \infty)[/tex] for function [tex]\sqrt {x-2}[/tex] , as for all values greater than 2, the function is defined.
- [tex](-\infty, \infty)[/tex] for function [tex]2\sqrt[3]{x}[/tex] as it is defined for all values of x.
- [tex](-\infty, \infty)[/tex] for function [tex]\sqrt[3]{x-2}[/tex] as it defined for all the values of x.
Now, the domain of given function matches with the function [tex]\sqrt {2x}[/tex].
Therefore, function [tex]\sqrt {2x}[/tex] has same domain as the given function. The domain of both the functions is [tex][0,\infty)[/tex]. Correct option is A.
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