Question

what is the domain of the function y=4sqrt2x+6

Answer 1

well, just bear in mind that a negative number inside a square root, gives you an imaginary value, so, what they're really asking is

What values can "x" take inside the square root that will not make it give a negative number

Answer 2

0 is ok, \(\large \sqrt{0}=0\) so that's ok

Answer 3

so, what do you think?

Answer 4

\[y=4\sqrt{2x+6}\]

a.\[x \ge 3\]

b.\[x \ge -3\]

c. \[x > \]

d.\[x \ge \frac{ -1 }{ 3 }\]

Answer 5

so, what do you think? which values can "x" have without yielding a negative value inside the root?

Answer 6

i dont know how to do this very well, square roots have alwasy confused me

Answer 7

ok, lemme put it differently, let's say \(\sqrt{2x+6}=\sqrt{0} meaning 2x+6=0

if 2x+6=0, what would be the value of "x"?

Answer 8

woops

Answer 9

ok, lemme put it differently, let's say \(\large \sqrt{2x+6}=\sqrt{0}\) meaning 2x+6=0

if 2x+6=0, what would be the value of "x"?

Answer 10

well it would have to be a negative value right?

Answer 11

dunno

Answer 12

-6 right?

Answer 13

let's see, 2x+6=0 .... what is "x" there?

Answer 14

well, 2x=-6, then divide both by 2

Answer 15

-3?

Answer 16

right, so 2x+6=0 WHEN X=-3, so
if "x" goes BELOW that number, -3, 2(-4)=-8, ==> -8+6=-2 or \(\large \sqrt{-2}\), which is a no-dice for a square root

Answer 17

so b.?

Answer 18

so, for the function to "work", "x" has to be ABOVE that number, -3
and that's your answer

Answer 19

yes, b) :)

Answer 20

so \[x \ge -3\]

Answer 21

thank you can i have help with a couple more?

Answer 22

sure, just post them in the channel, so we all can see it and help and revise each other :)

Answer 23

what is the domain function
\[y=4\sqrt{2x-5}\]

a. \[x= \ge \frac{ 5 }{ 2 }\]

b.\[x \ge \frac{ 2 }{ 5 }\]

c.\[x \ge -\frac{ 5 }{ 2 }\]

d.\[x> -\frac{ 5 }{ 2 }\]

Answer 24

do the same procedure
when they talk about the DOMAIN, they mean what values can the "independent variable" can take and yield a valid expression

in the case of roots, for EVEN roots, the number inside it, CANNOT BE negative

Answer 25

so, find out where the expression = 0, and find "x" from there, then you know when "x" is THAT VALUE, the expression is 0, and if "x" goes BELOW OR ABOVE that, it'd be negative.

so once you know where the expression is 0, and what "x" is, use the next number for "x" and see what the expression gives

Answer 26

it would be - 2.5? right?

Answer 27

so, when this expression = 0, what's "x"?

Answer 28

which would be -5/2 which would be d? right?

Answer 29

well, "x" can be equal to \(\large \frac{5}{2}\) , at that value you get 0 and \(\large \sqrt{0}=0\)

Answer 30

x>SOMETHING, means "x" HAS TO BE greater than SOMETHING

Answer 31

\(\cfrac{-5}{2}\) I meant :|

Answer 32

so am i wrong? im sorry im realllllyyy bad at math

Answer 33

"x" can be equal to \(\large \cfrac{-5}{2}\) , it can't go below that though, it can go above though

Answer 34

so its d?

Answer 35

http://01.edu-cdn.com/files/static/learningexpressllc/9781576855959/ALGEBRA_BOOT_CAMP_12.GIF

Answer 36

see the differences? :)

Answer 37

ik that... its a???

Answer 38

yes, it'd be "a" because that says "x" CAN BE EQUAL TO \(\large \cfrac{-5}{2}\) OR GREATER, and the root would still be non-negative

Answer 39

can you help me with more?

Answer 40

what is sin A fot the triangle shown

Answer 41

http://v-fedun.staff.shef.ac.uk/Trigonometry/images/Fig3.png

Answer 42

on that picture, the angle being used is "c"
you could say, you're EYEING from "c"

for your triangle, put your EYE on "a", who is your opposite and who is your hypotenuse?