What is the domain of f(x)=csc(x) ?

The domain of f(x)=csc(x) is 2pin<x<pi+2pin\lor pi+2pin<x<2pi+2pin

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domain of f(x)=csc(x)

domain

f (x) = csc (x)

2 πn < x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Interval Notation

(2 πn, π + 2 πn) \cup (π + 2 πn, 2 π + 2 πn)

Solution steps

Take the denominator(s) of

csc (x)

and compare to zero:

x = 2 πn, x = π + 2 πn

Periodicity of

csc (x) : 2 π

Combine period:

2 πn \leq x < 2 π + 2 πn

and undefined points.

The domain is

2 πn < x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

f (x) = \frac{9 e ^{x}}{e ^{x} - 5}

f (x) = x^{\frac{1}{7}} (x + 8)

f (x) = \frac{4}{x - 1}

\frac{8 x + 9}{x + 8}

f (x) = x^{2} + 2 x + 5

What is the domain of f(x)=csc(x) ?
The domain of f(x)=csc(x) is 2pin<x<pi+2pin\lor pi+2pin<x<2pi+2pin