The function f(x) = cot x is discontinuous on the set

The correct option is:

$$\{x=n\pi ,n\in Z\}$$

To understand why this is correct, we can analyze the definition of the cotangent function. The cotangent function,

$$f\left(x\right)=cotx$$

is a trigonometric function defined as the ratio of the cosine function to the sine function:

$$cotx=\frac{cosx}{sinx}$$

A function is discontinuous at any point where it is not defined. Since division by zero is undefined in mathematics, the cotangent function will be discontinuous at all values of

$x$

where the denominator is equal to zero. Therefore, we set the denominator to zero:

$$sinx=0$$

The sine function is equal to zero at all integer multiples of

$\pi$

which gives the general solution:

$$x=n\pi$$

where

$n$

is any integer. Thus, the cotangent function is discontinuous on the set:

$$\{x=n\pi ,n\in Z\}$$