Final answer:
The domain of the function (2x+7)/(x²-49) is all real numbers except x = 7 and x = -7, represented in interval notation as (-∞, -7) ∪ (-7, 7) ∪ (7, ∞).
Step-by-step explanation:
The domain of a function f(x) = (2x+7)/(x²-49) represents all the values of x for which the function is defined. In interval notation, finding the domain involves identifying all the x-values where the function does not have any issues like division by zero. Since the denominator is x²-49, which factors to (x-7)(x+7), we cannot have x = 7 or x = -7 because these would make the denominator zero.
Hence, the domain in interval notation is (-∞, -7) ∪ (-7, 7) ∪ (7, ∞), which means the function is defined for all real numbers except x = 7 and x = -7.