00:01
Exercise 62 on chapter 3, section 1, and we want to determine the domain of f of x equals x minus 1 over the absolute value of 3x minus 1 minus 4.
00:17
So remember we start off usually with all real numbers as our domain, but then we just have to remember two special cases.
00:26
If there is a denominator, we need to exclude all values of x that make the denominator.
00:31
That makes the denominator equal to zero.
00:34
And then if there's a radical with even index, we need to exclude all values that make the radican negative.
00:42
So when what we're going to do is we have a fraction for this problem.
00:48
So what we want to do is we want to take the denominator of this particular fraction and we want to set it equal to zero to determine any value that will make this expression zero.
01:04
So we're going to add four to both sides, and we got absolute value of 3x minus 1 equals 4, and we're going to go ahead and solve this absolute value equations by creating our two cases.
01:24
You want to know when the expression in the absolute value is equal to 4, and when the expression in the absolute value is equal to negative 4, because both numbers, the absolute value of 4 and the absolute value of negative 4, equals positive 4.
01:41
So now we're going to go ahead and solve 4x in both of these equations.
01:48
So let's start with the first one on the left...