yamyam70 one year ago Someone Check my work! Determine the Domain See drawing below

1. yamyam70

|dw:1437320720884:dw|

2. yamyam70

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

3. Michele_Laino

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

4. Michele_Laino

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

5. yamyam70

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 ?

6. Michele_Laino

yes!

7. yamyam70

lol give me a moment Im trying to think about it

8. yamyam70

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

9. Michele_Laino

both of those conditions have to be checked

10. yamyam70

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

11. Michele_Laino

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

12. yamyam70

$4 \ge x$

13. yamyam70

its [ 0 , 4 ] is it ?

14. Michele_Laino

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

15. Michele_Laino

that's right!

16. yamyam70

in overview Im getting the intersection of both conditions right ?

17. Michele_Laino

yes!

18. yamyam70

I LOVE YOU

19. Michele_Laino

thanks! :)

20. yamyam70

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

21. Michele_Laino

:)