00:01
Hello, so here we're given the function, f of x of x minus 2, divided by the square root of 7 minus x.
00:07
So for the domain, we have to have the, what's inside the square root must be greater than equal to 0, but we also are not allowed to divide by 0.
00:17
So therefore, we have to have, well, 7 minus x must be, well, it must be greater, strictly greater than 0, right? because 7 minus x cannot be equal to 0.
00:28
So we have to have that 7 minus x must be strictly greater than 0.
00:34
And we also must have that x minus 2 must be greater than or equal to 0.
00:38
Well, if 7 minus x is greater than 0, this is going to imply then that if we just will subtract 7 from both sides, we get negative x is going to be greater than negative 7, divided by negative 1, giving us x is then less than 7.
00:59
So x here must be strictly less than seven, right? because 7 minus a number less than 7 minus a negative we're going to be adding.
01:11
So x must be less than 7.
01:13
And we have to have that x minus 2 must be strictly greater or greater than or equal to 0, adding 2 giving us that x is greater than or equal to 2...