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$73-78=$ Domain Find the domain of the function. …

04:07

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Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69 Problem 70 Problem 71 Problem 72 Problem 73 Problem 74 Problem 75 Problem 76 Problem 77 Problem 78 Problem 79 Problem 80 Problem 81 Problem 82 Problem 83 Problem 84 Problem 85 Problem 86 Problem 87 Problem 88 Problem 89 Problem 90 Problem 91 Problem 92 Problem 93 Problem 94 Problem 95 Problem 96 Problem 97 Problem 98 Problem 99 Problem 100 Problem 101 Problem 102 Problem 103 Problem 104 Problem 105

Problem 75 Hard Difficulty

$73-78=$ Domain Find the domain of the function.
$$g(x)=\log _{3}\left(x^{2}-1\right)$$

Answer

$D_{g}=(-\infty,-1) \cup(1,+\infty)$

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Video Transcript

So we're testify. Name the domain of this function here. To do this, we need to find when Jia Vex is undefined. If you remember, basic longer than rules lob rhythms air on ly defined when the values that you and turn into them are positive. So in this case, we need to find when X squared minus one is greater than zero. Now we're first going to try and find out when it's equals zero. So we're gonna factor this out X minus one times X plus one Ziegel to zero. Now we're going to find the values of X that make this statement zero. So in this case, X is equal to one and negative one to make our lives easier. I'm going to make a number line, negative one and one. So now we're going to test values to see if this X squared minus one we'll stay positive. So we're going to enter a negative, too, into that X squared minus once. So when X is equal to negative too, we have negative too squared minus one. This will be four minus one equal to three. So in this case it's positive, which means it's defined Now we're going to plug in the value like zero. So an ex sequel to zero, we have zero squared, minus one negative one. So in this case, it's negative. So it's not going to be defined between negative one and one. Now we're gonna try values above one. So X is equal to two, so we'll do two squared minus one for minus one equals three. So this value here is positive. So in this case, our domain of our function, it's going to be negatives infinity all the way to negative one union with one and positive infinity, and that is the domain of our function.

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