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Answers

The domain of $\mathrm{f}(\mathrm{x})=\sqrt{\log \frac{1}{|\cos \mathrm{x}|}}$ is (a) $\mathrm{R}$ (b) $\mathrm{R}-[-\pi, \pi]$ (c) $\mathrm{R}-\left\{\mathrm{x} / \mathrm{x}=\frac{(2 \mathrm{n}+1) \pi}{2}, \mathrm{n} \in \mathrm{Z}\right\}$ (d) $\mathrm{R}-[-\pi / 2, \pi / 2]$

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Question 1 96. So we have to find out which of these four options is correct. Just for swine F of ethics, for f of ethics, uh we're going to replace its by ethics. So it's gonna look like one or 1, 1/1 minus 1/1 minus. So that's gonna be 1/1 minus x minus 1/1 minus six.

So that's going to be x minus one over X. So since sexism, denominator definitely uh X will take all the animals of real number except zero. And since the domain of Fx excludes X equal to one. So this is the domain for F of Fx. So uh If we talk about option eight, an option, it would be the correct choice.

Because it's saying that the domain of uh F of Fx is uh all the real values except zero and 1 stop aboard option B. So it says it asks us to find a five of F of negative two. So F f f X is already given, as is already found us x minus one. Or excerpts replace negative two. So they're gonna get three or 23 or two is again a correct choice.

Option B is also correct. Let's talk about option this is option B. And this one of the option a struggle board options see, so option C is F F F F F X O F of F of fx is gonna be uh function. Well, we already have f of effect. So in order to point F of f of effects, we're going to replace X by F off effects, which is x minus one or X.

So that's gonna be one or uh one over X. So that's going to be just X. So uh since f of effects has the domain and all the real values. Uh So uh this uh it's domain is gonna be same as the domain of F f F X. So it will take All the values except zero and 1.

So but but it has given that the domain of F of F of effects. Uh So the domain of ff ff effects, the same as that of effects of the domain of effects is all real values except one. And that's what has given over here. So this is also a true statement is correct. These correct, sees correct.

And Now we can easily find this by replacing X x five, so definitely will get wife. So option B is also correct. Thank you..

In this question which is us to find the domain. Oh the function that is for taxes. It was too Global basis. Model effects and the number is 18. Okay, so first of all I am going to define here.

The law. Okay. The definition says that if we have any function that is in law ethnic. That is why he was to vlog except basic than it is defined only if you satisfy some conditions that if this number should be positive, the base should be positive and you're This cannot be was 2 1. Okay.

So to apply these three conditions and then only the law function is different. Okay, now in our case we can see that we have the function effects if it was true lot more or less sex. It obviously this is it that is fixed and it is a positive number. So we have to apply all the conditions on the days here. So I can say that the base that is model of sub X should be better than zero and Models of X should we not? It was 21 Okay, but you can see that down here.

The models of X should be greater than zero. So you can see Models always remains better than zero. Okay. If you don't take zero here, so this shows that you cannot take the value of X. It was 20 Okay.

And this second condition says that model sex should not be close to one minute. Sex cannot be close to minus one or one. Okay, So I can say that these three values are not allowed in the domain. So finally the domain here is ar minus there to remove these three values that are minus 10 and one. Okay, this is the answer for the given question here.

And you can see that this answer is in the option number be here. So option #2B is the correct solution for the given question here. Okay, 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..

This problem for each of the given statements. We want to find it only in fortune is true and the domain for distance on a we have everyone speaks hindi and so domain words that would be true. The India, okay. For the most part of India, that's the national language there in India place where would be false? Will be in the United States, Everyone does not speak in the, we know that to be true because I don't speak hindi and I'm in the United States On the, we have their someone older than 21 years and so this can be at a university. Okay, that would be true at a university now where that would be false is the students and Canada Students in Canada and there is not a student in Canada and that's older than 21.

Let's say we have every two people have the same first name, it must be true. For the set of all johns all john's have the same first name of john that would be false. And I'll use the set of all americans instead of all the USa members. Yeah, authorities say citizens and I d we have someone knows more than two people. If someone knows more than two.

So that would be true. I'm just going to re do a repeat here and then be true at a university. Someone knows more than two people where that would be false. It would be the set of just me. Okay.

If my domain is just me that I don't know two other people in that domain. And so that would be false, and that's what..

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