Final answer:
The correct answer is option a) (-∞, 14) U (14, ∞).To determine the domain of a function, we need to identify any values of x that would make the function undefined.
Step-by-step explanation:
To determine the domain of the function f(x) = (x² + 121)/(x - 14), we need to identify all x-values for which the function is defined. The function is undefined where the denominator equals zero, which is when x = 14. Thus, the domain includes all real numbers except x = 14.
In interval notation, this is expressed as two intervals: from negative infinity to 14 and from 14 to positive infinity, not including 14 itself. In this case, the function f(x) has a denominator of (x - 14), so it would be undefined when x = 14. Therefore, x cannot be equal to 14. The domain of f(x) is all real numbers except 14, which can be represented as (-∞, 14) U (14, ∞).