00:01
All right, and this problem, we're looking at a function essentially that has a restricted domain.
00:06
So we have t of g equals 1 ,815 plus 0 .15 times g minus 18 ,150.
00:13
And they do tell you that t represents your federal income tax dollars.
00:19
And if you're married filing jointly, your taxes, and then g would be your adjusted gross income, what might you contribute together as a couple? but the only particular equation that adjusted gross income has between $18 ,150 and $73 ,800.
00:37
Okay, so it only works between those values.
00:40
All right.
00:40
So question or part a of the question is asking for what is the domain for t? remember domain is the set of x values for the function? okay.
01:01
And essentially, this problem actually kind of gave you the answer.
01:04
So right here would be the domain.
01:07
They're telling you between what two numbers this function works for.
01:10
So that would be our domain.
01:12
Now i'm going to write this in two ways.
01:15
I'm going to use the standard, you know, inequality they have right here.
01:18
So we got 18150 is less than g is less than or equal to 73 ,800.
01:25
If they do ask for it in interval notation, i'm not sure if it does or not.
01:29
We can also use brackets right here.
01:31
We're going to do 18150 print this.
01:34
I print a comma, and then 73 ,800, and then another bracket because you're including those numbers.
01:39
So it depends on how you want the answer, but technically either one of these are right.
01:43
So in order for this function to be true, it has to be between $18 ,150 and $73 ,800, what you're plugging in for g or for x.
01:54
All right, b's asking for, given that the tax value tax duty is increasing, the linear function is modified to adjust as gross income.
02:02
I want to find that range.
02:04
Okay.
02:05
So range would be, well, yvis exists would be the opposite of domain.
02:20
So this part right here, they actually did not give it to you, but they kind of gave you stuff to help with.
02:24
So in order to figure out what that range is, i'll get the plug of those domain values.
02:28
So for the first part of the range, i'm going to do t of $18 ,150 because that's where the domain starts.
02:35
And essentially what i'm doing is wherever there is replacing that with $18 ,150.
02:43
All right.
02:43
So we're a doing 1815 plus 0 .15 parentheses 18150 minus 18150.
02:57
I have worked that out because this will essentially right hand side technically be zero, you get $1 ,815.
03:03
Okay, so for the range of this one, then the beginning part of the domain are the same, just happened to the same number.
03:09
The second, the ending part of the domain, which are range, which would be the second part of the domain that we have to use, was that 7333.
03:16
$2 ,800.
03:18
So the same thing, wherever i see a g and replacing it with that 73 ,800.
03:33
If you just use a calculator, help you figure out what those numbers are, be really hard, subconscious to know what they are.
03:37
So this one end up being $10 ,162 and 50 cents.
03:45
All right, so to state our range for this, and again, i can use it as inequalities or an interval would be 1 -815 less than t, not g this time.
04:03
Less than equal to 10 ,1062 .5.
04:07
Okay, if i ask for an interval notation, we're just doing a bracket, because it includes those numbers, bracket 151, 1 ,815 comma, and then 10 ,10062 .5, and then a bracket.
04:27
Part c is asking for the adjusted gross income, g as a function of t...