Question

pleases help me!!!!!
Is it possible for x = −2 to be in the Domains of the functions
a) R(x) =3x^3-5x+6/x+2
b) H(x)=√x+1
Explain why or why not for each function.
What are the Domains of the functions R(x) and H(x)? If required, use inf for ∞.

Answer 1

if you plug -2 in for x in equation a what would you end up with in the denominator?

Answer 2

4?

Answer 3

-2 + 2 = ?

Answer 4

0 sorry

Answer 5

yep so if you divide by 0 what kind of answer does that give?

Answer 6

0

Answer 7

no, if you divide by zero the answer is "undefined"

Answer 8

ok so knowing that, here is the definition of the domain of a function , from wikipedia, "the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined"

Answer 9

so the domain is only inputs for which the function is defined, but for function a if we plug in a -2 then the answer is "undefined" so therefore is -2 in the domain of function a?

Answer 10

so -2 cannot be the domain or either one,right?

Answer 11

it cannot be in the domain of a for sure, because divide by zero is "undefined", what about function b?

Answer 12

no i think

Answer 13

because?

Answer 14

because it'd leave u with an irrational right?

Answer 15

well it would leave you with a complex/imaginary number which technically i think would be in the domain, but i think the answer your teacher is looking for is that is

NOT in the domain

Answer 16

ok good so you have the first question done what about the second part, what are the domains of each function?

Answer 17

i dont know

Answer 18

ok so lets look at equation b first, what type of numbers for x would give us a complex/imaginary answer?

Answer 19

negative numbers

Answer 20

correct, so the domain would be all numbers 0 or greater, right?

Answer 21

yes

Answer 22

perfect so that would look like this

x greater than or equal to 0

Answer 23

now how about equation a, there is only one number, -2, that would give us a divide by zero

Answer 24

so what would the domain look like for a?

Answer 25

x<-2?

Answer 26

yes but also greater than -2

Answer 27

i think you need to write both answers in interval notation

Answer 28

can you write this in interval notation? x is all numbers less than -2 and all numbers greater than -2

Answer 29

i get A but not B

Answer 30

oh, good, what did you get for A?

Answer 31

a: [0,inf)

Answer 32

hmm thats the answer for b

Answer 33

whoops yeah, i get B but not A

Answer 34

oh ok

Answer 35

so b, you need to use a union symbol

Answer 36

looks like a U

Answer 37

how would you show all numbers less than -2?

Answer 38

wait, just got completely confused

Answer 39

k

Answer 40

okay sorry bout that

Answer 41

no prob, ok so for a lets do that in two steps, how can you show that x is all numbers less than -2?

Answer 42

x<-2

Answer 43

i mean in interval notation

Answer 44

like this (-inf, -2)

Answer 45

ok but x is also all numbers greater than -2

Answer 46

so we need to write it like this

(-inf, -2) U (-2, inf)

Answer 47

does this make sense?

Answer 48

yes, theres brackets on -2 tho,right?

Answer 49

there is not brackets on the -2 because -2 is not included in the domain

Answer 50

okay

Answer 51

so since its not included we use parenthesis

Answer 52

nice, all done :)

Answer 53

i thnk i got it, thanks so much!

Answer 54

yw