Final answer:
The domain of the function is all real numbers except x = 4/3. The range of the function is all real numbers except y = 0.
Step-by-step explanation:
The given equation is y = 1/(3x-4).
To find the domain and range, we need to consider the restrictions on the variables.
Domain:
The denominator 3x-4 cannot be equal to zero, as division by zero is undefined. So, we need to solve the equation 3x-4 = 0 to find the value of x that makes the denominator zero.
Solving this equation, we get x = 4/3. Therefore, the domain of the function is all real numbers except x = 4/3.
Range:
The range is the set of all possible values of y for the given equation. Since the numerator is always 1, the range of the function is all real numbers except y = 0 as division by zero is undefined.