Final answer:
The domain of the function is all real numbers except 28, and the range of the function is (-∞, -3) ∪ (3, ∞).
Step-by-step explanation:
The domain of a function represents the set of all possible input values, while the range represents the set of all possible output values. To find the domain of the function f(x) = 3x / (28 - x), we need to consider any restrictions on the input values. In this case, the function is undefined when the denominator (28 - x) is equal to zero, since division by zero is not possible. Therefore, we solve for x in the equation 28 - x = 0, which gives us x = 28. The domain of the function is all real numbers except 28, so it can be written as (-∞, 28) ∪ (28, ∞).
To find the range of the function, we need to determine the set of all possible output values. One way to do this is by analyzing the behavior of the function as x approaches positive and negative infinity. As x gets very large in the positive direction, the function approaches 3. As x gets very large in the negative direction, the function approaches -3. Therefore, the range of the function f(x) = 3x / (28 - x) is (-∞, -3) ∪ (3, ∞).
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