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State the domain and range of the function.y = cotA) 2n+1 all real number such that X # T where n is an integer Domain Domain = all real number such that X# (n+l)z ...

Question

State the domain and range of the function.y = cotA) 2n+1 all real number such that X # T where n is an integer Domain Domain = all real number such that X# (n+l)z where n is an integer B) 6n +1 C) all real number such that Xt where n is an integer Domain 6n+1 D) all real number such that X # where n is an integer Domain

State the domain and range of the function. y = cot A) 2n+1 all real number such that X # T where n is an integer Domain Domain = all real number such that X# (n+l)z where n is an integer B) 6n +1 C) all real number such that Xt where n is an integer Domain 6n+1 D) all real number such that X # where n is an integer Domain



Answers

Fill in the blanks. The domain of $y=\cot x$ is all real numbers such that ______.

Let's take a look at the co tangent graph as it relates to domain. Remember, domain of a function is really just all possible input values. And when we look at a graph, those input values are really just the values on our X axis, right? All those X values which X values correspond to a given. Why value? I could pick an X value here, See that that corresponds to a Y. I could keep going. I could pick all different X values to have them correspond to a Y. But anywhere I reach one of these vertical ascent oats. All of a sudden, there's no why value that's defined. There's an undefined Why value for those given exes. Okay, well, anywhere else exit has a Y. How do I write that as my domain? Okay, well, I'm going to start off saying that the possible X values go across all real numbers when you use that are to define all real numbers, but X cannot equal anywhere. We have a vertical ascent toe and how do we know where that it was? How do I define that? Let's take a second and look at those vertical Assam toast we have asked. Um, totes add it looks like negative two pi negative pie zero pie two pi And you could guess that's going to continue both directions. Three pi four pi five pi Negative three Negative for negative five. It's going to keep going on forever as this graph continues to repeat itself. How I generalize that statement. Okay, well, I'm gonna refer to that as n pi. Hey, where n is just representing an integer there. Okay, so our domain, it's all real numbers, but ex cannot equal n pi where n represents that integer Those are all the possible inputs that we have a defined output for.

Okay, let's look at a quick sketch of our co tangent graph to figure out what goes in the blank here. So remember that the co tangent graph has these curves that go down with vertical sn toads in between. So there's a vertical s and toted pie, and at zero and then again at two pi loops and then again at negative pie, another vertical Lassen tote and again at negative two pi etcetera. There will be infinitely many of them and notice they occur it. Zero pie one pie two pi three pie Negative one pie negative two pi negative three pie always multiples of pi. So for the domain of this function, we have all real numbers such that X is not equal to a multiple of pie and the way we can express a multiple multiple of pious weaken, say n times pi where n is any integer

Yeah, high in the given question will find the function. The function is given as a wife square root law one over and more to live signing. How we can find domain for this function. Mhm. The main function be happier. That is Suero. The spread of X. We have the venus coming out to be X. Greater than or equal to do. So you get one point here. That is low one over model A cynic that's coming out to be greater than he quoted zero. Now, if you look at the Lord granted like this, this is one and a gold still internally. Right? So you can see here low function is greater than Or equal to zero. That is for 1:20 minutes. Right? So therefore domain for this function log one over model of cynics. So one role model of cynic should lie between the one less than equal to one over model of cynics. There's less than internet. That's the interval we get now. So ultimately we get to the value of acts for which this function is define now if we take a recipe of all of this given inequality. So we get one less than equal to I'm sorry. We can want greater than equal to find changes because of the english program. So more or less cynics. It's great. But then no one over intrigued that is coming out to be zero. Now it's a mortal sin X. The first we use foster design and then build negative sign. So we get to inequalities accordingly. So we have one more than equal to cynics greater than deal and taking we get one more than equal to negative cynics Earth. Wait and then zero. So the one interval we get here. Finex lying between one more than equal to Synnex where than zero and technologies coming out to be negative one less than equal to cynics less than zero. So if you combine these two intervals, we get to me that is coming out to be okay activated. The domain for one over mortal cynics. So for signing it will be the range. So the radio sign next is coming out to be reach for findings. He's coming up with negative 1-0 lead. Only alluded to negative one Below zero. You don't want included Union zero. You know what? Right. The range for signing. That means from the screen it is quite clear that cynics can take all the values from negative 1 to 1. Including negative one and one. But cynics will not take the value as zero. We will have finished. There's no equal to zero for that that we have. Which option is there? So china is not equal to zero. That means act should not equal to zero and then plus -5, Love -2 by and for all, know which option that finds this. But we have all real values except the actual values, which X cannot take all the values except and by and belong to. In Egypt for coming up to be option C. Thank you.

In this question we have to find domain of the function and that is perfect for the worst one divided by x minus your testing data rex. Okay, so we did the function to be defined. If I can say that the non monetary is not big bus to zero. Okay. It means I can say their tax minus logistically dysfunction should not be close to zero means acts should not. It was to protest invader function. Okay now we know that X is it was too the attention to their function. It happens that I can say that in peter's Okay. Means I know that my ex is It was the greatest containers if I am going to take here and integer value X belongs to either zero either bless minus one. Either bless minus to plus minus three. Okay, Mediafax belongs to any interior value. The next should be. It was to its greatest interior function. Now we can say that it should not be, it was to protect you and the other functions. So the dimensions says that we have to Take all the real values but you cannot take your zero less -1. Less -2. Okay that's minus three because at these values he or denominated changes in 20 and the function gets on designed it can also be bitterness ar minus their dear. Okay that means interiors. So I can say that the out of the given options the C option is correct. Answer what they given question here. Okay thank you. Yeah.


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