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 ∞.

- anonymous

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- anonymous

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

- anonymous

4?

- anonymous

-2 + 2 = ?

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## More answers

- anonymous

0 sorry

- anonymous

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

- anonymous

0

- anonymous

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

- anonymous

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"

- anonymous

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?

- anonymous

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

- anonymous

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

- anonymous

no i think

- anonymous

because?

- anonymous

because it'd leave u with an irrational right?

- anonymous

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

- anonymous

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

- anonymous

i dont know

- anonymous

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

- anonymous

negative numbers

- anonymous

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

- anonymous

yes

- anonymous

perfect so that would look like this
x greater than or equal to 0

- anonymous

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

- anonymous

so what would the domain look like for a?

- anonymous

x<-2?

- anonymous

yes but also greater than -2

- anonymous

i think you need to write both answers in interval notation

- anonymous

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

- anonymous

i get A but not B

- anonymous

oh, good, what did you get for A?

- anonymous

a: [0,inf)

- anonymous

hmm thats the answer for b

- anonymous

whoops yeah, i get B but not A

- anonymous

oh ok

- anonymous

so b, you need to use a union symbol

- anonymous

looks like a U

- anonymous

how would you show all numbers less than -2?

- anonymous

wait, just got completely confused

- anonymous

k

- anonymous

okay sorry bout that

- anonymous

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

- anonymous

x<-2

- anonymous

i mean in interval notation

- anonymous

like this (-inf, -2)

- anonymous

ok but x is also all numbers greater than -2

- anonymous

so we need to write it like this
(-inf, -2) U (-2, inf)

- anonymous

does this make sense?

- anonymous

yes, theres brackets on -2 tho,right?

- anonymous

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

- anonymous

okay

- anonymous

so since its not included we use parenthesis

- anonymous

nice, all done :)

- anonymous

i thnk i got it, thanks so much!

- anonymous

yw

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