Question

How do I: Express the domain of the given function using interval notation?
f(x)=x/ 15x^2 + 13x - 20

Answer 1

hey. do you mean f(x) = x / (15x^2 + 13x - 20) ?

Answer 2

yes

Answer 3

nevermind i solved it thanks

Answer 4

i meant to ask a different question, sorry

Answer 5

is there another question you want to ask?

Answer 6

yes. it was determine domain and range using interval notation of
f(x)= radicand(x^2 -8x -9

Answer 7

\[f(x) = \sqrt{x^2 -8x -9}\]

Answer 8

just so you know i believe radicand refers to what is under the square root, but you mean square root of (x^2 -8x -9) right?

Answer 9

ok well for a square root function what you need to know is that what's under the square root can't be negative, because no real number multiplied by itself equals a negative

Answer 10

ok i understand so far

Answer 11

ok, so you want to try to factor that, to see where it is negative and where it is positive. you did the other problem so you know how to factor, right?

Answer 12

yes, i have x=-9 and x=1

Answer 13

that's not quite right, look at it again

Answer 14

is it 9 and -1 instead?

Answer 15

sorry, my browser crashed. yes, that's right. so you have sqrt ((x-9)(x+1)). what i like to do is draw a number line below that to help me see where the function is 0, negative, and positive

Answer 16

so draw a line, hashmarks at -1 and 9, and we know it's 0 at those points, so mark 0 above -1 and 9

Answer 17

now test a point on the left side, in the middle, and on the right to see if it comes up positive or negative

Answer 18

try x= -2. (-2-9)(-2+1) is a negative times a negative, so that's positive. so now i mark all +++ to the left of the first 0 on my line

Answer 19

you still here, is this helping?

Answer 20

im here thank you. how do you know what sign to use when determining if the equation is true?

Answer 21

what i mean is, you plug in -2 to the equation to see if its true right?

Answer 22

what do you mean by true?

Answer 23

(-2)^2 - 8(-2) -9=0 ?

Answer 24

or do you use an equality sign

Answer 25

no, we already know that the values that make what's under the square root equal to 0 are x = -1 and x = 9

Answer 26

that's what the factoring is for

Answer 27

by plugging in -2, we just want to see if that section of x-values comes up negative for y or positive

Answer 28

oh ok

Answer 29

remember the goal is to see which x-values make what's under the square root negative, because those are not part of the domain

Answer 30

so by plugging in -2, we get 11. then what from there?

Answer 31

it doesn't matter what the number is, we just care that it's positive, so did you draw the number line like i said? do you understand what i mean by that?

Answer 32

yes

Answer 33

so since they're both positive, that means what for interval notation?

Answer 34

well -2 turned out positive, so that means that all values less than -1 turn out positive, so those will be part of the domain

Answer 35

but we still have to check the other intervals

Answer 36

the one in the middle comes out negative

Answer 37

and the last one comes out positive

Answer 38

yes that's right, so the domain is the positive part

Answer 39

ok so what does it look like in interval form?

Answer 40

ok (-inf, -1) U (9, inf) is what it will be

Answer 41

(-infinity,-1] [9,infinity)? something like that?

Answer 42

no, you're right

Answer 43

the brackets are right. (-inf, -1] U [9, inf) the U stands for union

Answer 44

got it! thank you for your help!

Answer 45

:)

Answer 46

no problem.