Question

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

Options

• {x = nπ : n ∈ Z}

• {x = 2nπ : n ∈ Z}

• `{x = (2"n" + 1)pi/2 ; "n" ∈ "Z"}`

• `{x = ("n"pi)/2 ; "n" ∈ "Z"}`

Answer 1

The function f(x) = cot x is discontinuous on the set {x = nπ : n ∈ Z}.

Explanation:

Given that: f(x) = cot x

⇒ f(x) = `cosx/sinx`

We know that sin x = 0 if f(x) is discontinuous.

∴ If sin x = 0

∴ x = nπ, n ∈ nπ.

So, the given function f(x) is discontinuous on the set {x = nπ : n ∈ Z}.