Final answer:
The domain of the function y = 1/x - 7 is all real numbers except x = 0.
Step-by-step explanation:
The domain of a function is the set of all possible inputs, or x-values, for which the function is defined. In this case, the function is y = 1/x - 7.
The only restriction on the domain occurs when the denominator of the fraction becomes zero, since division by zero is undefined.
To find the domain, set the denominator equal to zero and solve for x: 1/x = 0 ⟶ x = 0.
Therefore, the domain of the function is all real numbers except x = 0.
In interval notation, the domain can be written as (-∞, 0) U (0, ∞).