anonymous
  • anonymous
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 ∞.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
if you plug -2 in for x in equation a what would you end up with in the denominator?
anonymous
  • anonymous
4?
anonymous
  • anonymous
-2 + 2 = ?

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anonymous
  • anonymous
0 sorry
anonymous
  • anonymous
yep so if you divide by 0 what kind of answer does that give?
anonymous
  • anonymous
0
anonymous
  • anonymous
no, if you divide by zero the answer is "undefined"
anonymous
  • 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
  • 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
  • anonymous
so -2 cannot be the domain or either one,right?
anonymous
  • anonymous
it cannot be in the domain of a for sure, because divide by zero is "undefined", what about function b?
anonymous
  • anonymous
no i think
anonymous
  • anonymous
because?
anonymous
  • anonymous
because it'd leave u with an irrational right?
anonymous
  • 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
  • anonymous
ok good so you have the first question done what about the second part, what are the domains of each function?
anonymous
  • anonymous
i dont know
anonymous
  • anonymous
ok so lets look at equation b first, what type of numbers for x would give us a complex/imaginary answer?
anonymous
  • anonymous
negative numbers
anonymous
  • anonymous
correct, so the domain would be all numbers 0 or greater, right?
anonymous
  • anonymous
yes
anonymous
  • anonymous
perfect so that would look like this x greater than or equal to 0
anonymous
  • anonymous
now how about equation a, there is only one number, -2, that would give us a divide by zero
anonymous
  • anonymous
so what would the domain look like for a?
anonymous
  • anonymous
x<-2?
anonymous
  • anonymous
yes but also greater than -2
anonymous
  • anonymous
i think you need to write both answers in interval notation
anonymous
  • anonymous
can you write this in interval notation? x is all numbers less than -2 and all numbers greater than -2
anonymous
  • anonymous
i get A but not B
anonymous
  • anonymous
oh, good, what did you get for A?
anonymous
  • anonymous
a: [0,inf)
anonymous
  • anonymous
hmm thats the answer for b
anonymous
  • anonymous
whoops yeah, i get B but not A
anonymous
  • anonymous
oh ok
anonymous
  • anonymous
so b, you need to use a union symbol
anonymous
  • anonymous
looks like a U
anonymous
  • anonymous
how would you show all numbers less than -2?
anonymous
  • anonymous
wait, just got completely confused
anonymous
  • anonymous
k
anonymous
  • anonymous
okay sorry bout that
anonymous
  • 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
  • anonymous
x<-2
anonymous
  • anonymous
i mean in interval notation
anonymous
  • anonymous
like this (-inf, -2)
anonymous
  • anonymous
ok but x is also all numbers greater than -2
anonymous
  • anonymous
so we need to write it like this (-inf, -2) U (-2, inf)
anonymous
  • anonymous
does this make sense?
anonymous
  • anonymous
yes, theres brackets on -2 tho,right?
anonymous
  • anonymous
there is not brackets on the -2 because -2 is not included in the domain
anonymous
  • anonymous
okay
anonymous
  • anonymous
so since its not included we use parenthesis
anonymous
  • anonymous
nice, all done :)
anonymous
  • anonymous
i thnk i got it, thanks so much!
anonymous
  • anonymous
yw

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