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1.1EP Score: 15/30 15/25 answeredQuestion 17Give the domain ofn(r)3z In Interval notation.Submlt Questlon...

Question

1.1EP Score: 15/30 15/25 answeredQuestion 17Give the domain ofn(r)3z In Interval notation.Submlt Questlon

1.1EP Score: 15/30 15/25 answered Question 17 Give the domain ofn(r) 3z In Interval notation. Submlt Questlon



Answers

Find the domain of the indicated function. Express answers in both interval notation and inequality notation. $k(z)=\frac{z}{z-3}$

All right. Welcome back. So for this problem where he had the function years, you equals Z divided by Z minus three. All right, so we can see that this function will be volatile, would rate when Z is equal to three. Because when Z is equal to three the denominator eight year, this stuff will be equal to zero. That is bad when we're dividing by zero. So we don't want that to happen. So we can say that just not acquitted. Three. Where we can also write this as this set from negative infinity to three. You're munis it from three to your infinity. Not that we're using parentheses right here instead of braces or brackets, because must so that we don't include the value three.

So in this question were given a function HFC and asked to find the domain. So in questions like this, I always first try to look for the conditions that would cause undefined answer when we we um plug a domain value into the function. So basically what would Z have to be for this equation to give us an undefined answer? In this case the denominator yeah. Mhm. Mhm would have to be equal to zero in order for us to get an undefined answer because two divided by zero is going to be on defined. So to figure that out, we can simply figure out what value for Z in this denominator right here would give us zero. So in this case it would be four. So if these four then our answer or denominator is going to be zero and by default or function is going to be undefined. So when we look at the inter violent inequality expression of our domain, let's start with inequality Z cannot be four. That's the only condition that would result in an undefined answer. So for interval it's gonna look like this. Z can be any number from negative infinity. Up to four. For not included. So we're going to use regular brackets, or Z can be any number after four. Up to infinity. Yeah.

For the domain of this traction. Here, you know that the denominator three x minus 12 cannot equal zero because we cannot divide by zero. So this means that the reacts cannot be equal to 12 or ex cannot be equal to four in a debilitation. We have the X It belongs to from negative infinity before and then from four to infinity.

All right. Welcome back for this problem. We're looking at the function H Z is equal to two to find a wife for minus c. All right, so looking at this function, um, reconvene kind of looking to the future a little bit and see that there will be a problem when z is equal to four. When Z is equal to four or take a look at what happens. H of four is equal to about it by four minus four, which is equal to two divided by zero, which is undefined. All right, so we know that it does. He cannot be. For we can say that. Um you mean, what could start writing that over again? A couple of ways. We can write this out. Um, I cannot equal for and say Z is an element of the real numbers. When is for instead of four. We can also say that Z is from goes from negative infinity to all the way up to four bliss from or all They have to community kind of a fund where we can write this. We can write it as negative infinity for okay, that interval union or to infinity any of these ways are basically about about. This is probably the best way to write it right here. Who are our purposes?


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