00:02
Now, in this video, we've been given a piecewise function.
00:07
This function is called piecewise function because it is defined only within some ranges.
00:15
So within the range where x is less than or equal to negative 2, the function gives us 2.
00:21
Then we have negative x plus 1 all into bracket.
00:26
If the function is or the real number value x is between negative two and one and so forth.
00:36
Now, we've been asked to find the value of, first of all, if h is zero, if x is zero, what would be the functional value? now, if x is zero, then x is going to fall where? where will x fall? x is going to fall somewhere between negative 2 and 1.
01:05
Because 0 falls between negative 2 and 1.
01:09
So in that case, then we cannot take a function.
01:14
Let's actually write it somewhere here.
01:18
If x is 0, then remember we are going to actually get.
01:26
So you realize that 0.
01:30
Is going to fall within this range here.
01:33
Zero is going to fall within here.
01:36
Okay.
01:38
So the function will only be defined on this value.
01:45
Okay.
01:46
The function is going to be defined only within this value.
01:49
It will be undefined here.
01:51
It will be undefined here because zero only lies between negative two and one.
01:58
So quickly, we can take the range of value or what x is defined.
02:06
So if you have h of 0, then we're just going to substitute 0 here plus 1 raise the power 2.
02:15
And what is that going to give us? we're going to have negative 1 raise the power 2, which will still give us what 1.
02:23
So we will actually get negative 1.
02:29
So if we have x to be zero, then our value, our functional value is going to be what negative 1.
02:39
Now, the next questions that we should find, if h is 1, if h is 1, h is 1, let's go back to our function and see where 1 is defined...