Answer:
Step-by-step explanation:
To find the domain of the function (f-g)(x) where f(x) = 4x / (6x - 1) and g(x) = -2x / (-5x - 4), we need to consider the domains of both f(x) and g(x) individually.
For f(x) = 4x / (6x - 1), the denominator cannot be equal to zero:
6x - 1 ≠ 0
6x ≠ 1
x ≠ 1/6
For g(x) = -2x / (-5x - 4), the denominator cannot be equal to zero:
-5x - 4 ≠ 0
-5x ≠ 4
x ≠ -4/5
Now, the domain of (f-g)(x) will be restricted by the values of x that make the individual functions f(x) and g(x) undefined. So, the domain of (f-g)(x) is the intersection of the domains of f(x) and g(x).
Therefore, the domain for (f-g)(x) is x ≠ 1/6 and x ≠ -4/5.
This means the correct answer is:
b) ( x ≠ 1/6 ) and ( x ≠ -4/5 )
