Question

Help Please!!
Find the The domain of the function of 1/sqrt(9x+2) my answer after solving was [-2/3, infinity) When i asked for help my teacher gave me this cryptic response: "what has to be true of expressions in the denominator? Combine these ideas and your will get your answer!" I have no idea what she is talking about. Please help me.

Answer 1

Under the square root has to be positive, and the denominator cant be equal to 0.

so you could solve

9x+2>0

to get domain

Answer 2

i think that is what i did and for my domain i got [-2/3, infinity)
my set up was 9x=2 is greater than or equal to 0 and i solved that way

Answer 3

well if its greater than or EQUAL to then that could make the denominator 0 because sqrt(0) is 0 so it should just be greater than 0


So you had the right idea, but you shouldnt get -2/3 in solving for x

9x+2>0
9x>-2
x>-2/9

which would make the domain

(-2/9, infinity)

Answer 4

I typed in -2/9 on my homework but wrote it in wrong here. How come it's (-2/9, infinity) and not [-2/9, infinity)? I though if you had the end pt number then you could use [ for the sign

Answer 5

Well since the inequality says greater than, not greater than or equal to. -2/9 isnt actually included in the domain, just everything greater than it.

When the number is included in the domain you use a bracket
when the number isnt included you use parentheses

Answer 6

oh, that makes so much sense. Thank you so so so much!!

Answer 7

You're welcome