00:01
We have a function that is natural log of x square minus sorry x square by x minus 4 and we are supposed to find the domain of that particular function.
00:11
Now domain means any domain means any set of values that can be plugged into this particular function so that we get a result.
00:23
So it means in domain domain.
00:26
Domain is a set where this function is defined.
00:29
That is if we can get a result from this function.
00:31
For example, when it comes to log x, this means that log x is defined for any numbers that for x is greater than 0.
00:42
That means for any real positive number, we have a logarithmic value for that.
00:49
That means that x can never be 0 or negative.
00:53
So that particular condition exists here also.
00:56
For any number that goes less than 0 when it comes to x squared by x minus 4, we can't for this particular come for this total value we can't find the logarithic value of that so we just need to apply the condition here but one thing you need to note here is that this is a fraction so you will have to do a bit of thinking here so the first thing is that x square by x minus 4 the first thing that you need to think here is that if this particular numerator numerator of a fraction.
01:32
If numerator turns out to be for a fraction to exist, for a fraction to exist, it needs both numerator and denominator, right? so for this particular fraction or for any fraction when numerator becomes zero, the fraction is zero, right? fraction becomes zero.
01:57
When denominator becomes zero, then it is not defined or it is the fraction becomes infinity or the is not defined.
02:05
So hence two things that we need to consider here is that x square x square can never be zero which means that x can't be zero first thing.
02:22
Now the second thing you need to consider is that the denominator must not be zero.
02:26
That means the denominator that is x minus 4 has to be greater than 0.
02:35
Now you may ask me why it can be what if it is less than zero you just said that it is not it does not need to be equal to zero so what comes when it is negative what happens here is that when you take a when you just take a negative value for x say minus 2 x square here we have an x square that means it is only post we get we only get positive values so when we take a negative value for x the whole fraction becomes negative right that is minus two whole square it will become minus two whole square divided by minus two minus four that is four divided by minus six for any negative value this fraction will turn out to be negative right hence x minus four has to be greater than zero if for example if x if the number is less than 4, for example, 3.
03:39
Then also, this will be 9 divided by 3 minus 4, which means minus 9, right? 9 by minus 1, which is also a negative...