00:01
In this problem we are given with 10 different functions.
00:06
These are the functions given in the question.
00:10
And we need to find which of these functions are continuous on the set of all real numbers.
00:16
If any of them are not continuous on or, we need to find their particular values.
00:22
So how are we going to do that? first of all, understand that whenever we have a function of the form, g of x divided by h of x, if we want to find where this function is not continuous, we need to equate the denominator to 0.
00:40
And the values which satisfies this equation or the points where this function is not continuous.
00:50
So consider the case where the function is of the form g of x divided by sum k, where k is a sum constant.
01:00
In such case we cannot equate the constant to be equal to 0 and find the values of x because there will be no xes in the constant k.
01:11
So in such case we can say that functions of this format will be continuous on r.
01:19
So let's observe the questions.
01:23
Here observe that the question number 1 and 3, 4 and 10.
01:31
These functions are of the form j of x divided by some k, where in this case, k is 1, here also k is 1, and this case k is 2 and here k is 1.
01:45
So these functions are continuous on r.
01:48
So what we can say is the problems 1, 3, 4 and 10 are continuous on r.
02:00
And for other functions we need to equate their denominator to be equal to 0 and find the values of x.
02:08
To do that, first, let's consider the function number 2 and in that case, the denominator is x square minus 4x plus 4 is equal to 0.
02:18
If we solve this equation, we will get x minus 2 the whole square is equal to 0, which implies that x is equal to 2.
02:26
Therefore, the second function f is not continuous at x is equal to 2.
02:35
Now, third and fourth are already continuous.
02:38
We already found that.
02:39
Now let's go to the question number 5.
02:41
Here, the function is x squared divided by minus of 3x plus 9...