Question

Someone Check my work!
Determine the Domain
See drawing below

Answer 1

or would that be [0 , 4] only if we consider the radical inside?

Answer 2

hint:
the inner radical exists if
\[\Large x \geqslant 0\]
furthermore we have the subsequent condition:
\[\Large 2 - \sqrt x \geqslant 0\]

Answer 3

that additional condition, is equivalent to this one:
\[\Large 2 \geqslant \sqrt x \]

Answer 4

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 ?

Answer 5

yes!

Answer 6

lol give me a moment Im trying to think about it

Answer 7

oh and I just found out that I cant make x negative

Answer 8

both of those conditions have to be checked

Answer 9

im thinking it should be all real numbers except , x would not equal to 0 and 4

Answer 10

hint:
starting from this inequality:
\[\Large 2 \geqslant \sqrt x \]
square both sides, what do you get?

Answer 11

\[4 \ge x\]

Answer 12

its [ 0 , 4 ] is it ?

Answer 13

correct! furthermore, as I wrote before, we have:
\[\Large x \geqslant 0\]
so, what can you conclude?

Answer 14

that's right!

Answer 15

in overview Im getting the intersection of both conditions right ?

Answer 16

yes!

Answer 17

I LOVE YOU

Answer 18

thanks! :)

Answer 19

now I feel confident in determining the D :)))))))

Answer 20

:)