Final answer:
The domain of ((f)/(g))(x) where f(x)=3x and g(x)=-5x+3, is all real numbers except x = 0.6, since division by zero is undefined.
Step-by-step explanation:
The domain of a function is the set of all possible input values or x-values that will make the function work.
For the division of the functions f(x) and g(x), you have to consider where the denominator g(x) is equal to zero, since division by zero is undefined.
Set g(x)=-5x+3 equal to zero and solve for x:
-5x + 3 = 0
Solve for x:
-5x = -3
x = 3 / 5 = 0.6
Therefore, the domain of (f/g)(x) would be all real numbers except x = 0.6.
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