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Determine the domain restriction; if necessary, so that f (x) = 7-26 one-to-one(2.0)(-m.-1)U(-[.0)No restriction necessarv(-o.-I)(-4,61...

Question

Determine the domain restriction; if necessary, so that f (x) = 7-26 one-to-one(2.0)(-m.-1)U(-[.0)No restriction necessarv(-o.-I)(-4,61

Determine the domain restriction; if necessary, so that f (x) = 7-26 one-to-one (2.0) (-m.-1)U(-[.0) No restriction necessarv (-o.-I) (-4,61



Answers

Find the domain of the function. $$f(x)=\sqrt{x^{2}-4 x-21}$$

Russian is asking about the domain off the given Function act or packs. So after eggs, ISS equals two X, divided by Esquire Route O X Esquire minus five X minus six So we need to find out the domain off this function. So for this access choir minus five, X minus six should be greater than or equals toe zeal. Now we can say that X Esquire minus two X minus three x. This is so This is no the part where you can see the composition of this function. Access choir, plus X minus six X minus six. Should be greater than it was +20 So from here, we can take excrement over here, so x plus one and minus six common from here. Then again, X plus one should bigger than any of us to do So. The factors for this equation are X plus one and X minus. Six should be greater than or so not because to CEO, this is strong. Over here not equals +20 So x plus one. My people I'd buy X minus six should be greater than zero only. So we can say that either X plus one should be greater than zero or X minus six. We get zero. So it should be greater than minus one and actually be greater than plastics. So this is the two parts of the solution. Now we need to find out the common values. This is a number line here. Zero. Here we have minus one here. We have six only toe actually be greater than six. So this is the part and actually bigger than minus one. And this is the part. So we can say that accident You should be greater than six. Only that is the domain for this function.

Physical number 26 in which we need to find the domain off F X equal to four x divided by 66 square plus starting X minus five. So, too many is all the values off X Ah, for which yeah, this is not zero. As if this becomes zero, FX will be undefined. So 66 square plus 13 x minus five should not be equal to zero. This is 6 to 5. 13. That is minus 30. Okay, we have to fact raise by anyhow. 65 30 15 and 2. 30. Okay, six sixes. Squad plus 15 x minus two works minus five should not be equal to zero. So this is three x two x plus five minus one two x plus five should not be equal to zero. That is two weeks plus five in 23 x minus. Film should not be equal to zero. So either two X plus five should not be equal to zero are three x minus one should not be equal to zero, so x should not be equal. Toe minds five by two x should not be equal to on by three. So domain will be minus and faint. E Tu minus five by two. Union minus five by two 21 by three Union on by three to infinity. Yeah, These are the well, its effects. That is the romaine. Thank you.

It's a problem. Number 30 door in, which means evil with evil. With the domain off. Have Mexico toe X minus tool X minus six under the Squire's out. So since this is under the square root oh, domain will be X minus two X minus six. Greater than equal to zero. Oh, key. So we'll be having two critical points two and six. So let us stronger number lane, toe six. If you plug in any value left side of two, that is, let us plug in zero here. So this will become positive. Any value that is three. This Look, I'm negative. This you looking positive. So we have to take care of this. So we'll be taking, uh, this interval this interval only so our domain will be okay. Ex belongs toa minus infinity to to union 62 and 20. Think is always

Uh huh. We have the function after black Sequels. Mhm. Four minus X squared. And we want to find universe effects. Then think about the best has a wide they change X and Y. So X equals four minus Y squared. It's all for why I'm going to add the Y squared over track X. Yes. Where so are inverse function is the square root of 4 -1. But this can only happen um from since our inverse function is a function which only exists when what's under the radical positive means X has to be greater than or equal to four. So however you may write that X. X greater than or equal to four or you might say um you know X is a subset from negative infinity to positive for included. Mhm. Yeah.


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