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