Someone Check my work! Determine the Domain See drawing below

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Someone Check my work! Determine the Domain See drawing below

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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|dw:1437320720884:dw|
or would that be [0 , 4] only if we consider the radical inside?
hint: the inner radical exists if \[\Large x \geqslant 0\] furthermore we have the subsequent condition: \[\Large 2 - \sqrt x \geqslant 0\]

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that additional condition, is equivalent to this one: \[\Large 2 \geqslant \sqrt x \]
If we consider both conditions , the inner radical and the whole radical, I need to make the inner radical exist, as well as meeting the subsequent condition, thats the rule right ?
yes!
lol give me a moment Im trying to think about it
oh and I just found out that I cant make x negative
both of those conditions have to be checked
im thinking it should be all real numbers except , x would not equal to 0 and 4
hint: starting from this inequality: \[\Large 2 \geqslant \sqrt x \] square both sides, what do you get?
\[4 \ge x\]
its [ 0 , 4 ] is it ?
correct! furthermore, as I wrote before, we have: \[\Large x \geqslant 0\] so, what can you conclude?
that's right!
in overview Im getting the intersection of both conditions right ?
yes!
I LOVE YOU
thanks! :)
now I feel confident in determining the D :)))))))
:)

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