Final answer:
The domain of the function f(x) = 1/(2x+8) is all real numbers except -4, as having x equal to -4 would cause division by zero, which is undefined.
Step-by-step explanation:
The student asked to determine the domain of the function f(x) = \frac{1}{2x+8}. The domain of a function includes all the possible values of 'x' that can be plugged into the function without causing an undefined situation, such as division by zero. In this function, as long as 2x + 8 is not equal to zero, the function will be defined. Solving the inequality 2x + 8 \\eq 0 gives us x \\eq -4. Thus, the domain of the function is all real numbers except -4.