00:01
Hi here for the given question we are given a function which is f of x, y is equal to square root of 5 minus x square minus ln of x minus 5.
00:15
Now here we need to consider the function and then we need to consider the region for the domain of the given function.
00:24
Now here we know that the domain can be calculated if we consider this two terms separately.
00:30
So here first of all we will calculate the term which is square root of 5 minus x square.
00:37
For example it will be equal to greater than or equal to 0.
00:41
The value will be always non -negative if we assume that x is a real number.
00:45
So this further implies we have 5 minus x square greater than or equal to 0, squaring both the sides.
00:51
This further implies here we have the value of x will be completely dependent on 5.
01:01
So here the value will be x square minus 5 less than or equal to 0 which further gives here we have x less than or equal to plus or minus under root of 5.
01:16
So here the value is depending on the value of plus or minus 5.
01:21
So this is for the first term.
01:23
Now here we know that x minus 5 is a natural log so x minus 5 will be greater than 0 for solution to be exist because we know that ln of 0 does not exist...