Final answer:
The function f(x) = csc(x) is not defined when x = 0 because it involves division by zero, which is undefined.
Step-by-step explanation:
The function not defined when x = 0 is f(x) = csc(x). The cosecant function, csc(x), is the reciprocal of the sine function, meaning csc(x) = 1/sin(x). Since the value of sin(0) is 0, taking the reciprocal would involve division by zero, which is undefined in mathematics. Therefore, the cosecant function is not defined at x = 0.
It is important to note that the secant function, sec(x), which is the reciprocal of the cosine function, is defined at x = 0 because cos(0) = 1, and taking the reciprocal of 1 is still 1, so sec(0) is defined and equals 1.