Final answer:
The domain of the function q(s) = 8s/(s-6) is all real numbers except s = 6. This is because the function is undefined when the denominator, s-6, equals zero. The domain in interval notation is (-∞, 6) ∪ (6, +∞).
Step-by-step explanation:
The student has asked to find the domain of the function q(s) = 8s/(s-6). The domain of a function is the set of all possible input values (in this case, s values) that the function can accept without yielding any mathematical errors. For this function, we must consider restrictions that would cause the function to be undefined, which happens in this particular function when the denominator is equal to zero.
In the case of the function q(s) = 8s/(s-6), the denominator s-6 becomes zero when s = 6. Therefore, our function q(s) is undefined at s = 6. To find the domain, we exclude this value from the set of all real numbers. The domain of q(s) is all real numbers except s = 6.
In interval notation, we represent this domain as (-∞, 6) ∪ (6, +∞), which means all real numbers from negative infinity up to 6, not including 6, and from 6 to positive infinity, again not including 6.