What is the domain of f(x)=2csc(2x) ?

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

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domain of f(x)=2csc(2x)

domain

f (x) = 2 csc (2 x)

πn < x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

Interval Notation

(πn, \frac{π}{2} + πn) \cup (\frac{π}{2} + πn, π + πn)

Solution steps

Take the denominator(s) of

2 csc (2 x)

and compare to zero:

x = πn, x = \frac{π}{2} + πn

Periodicity of

2 csc (2 x) : π

Combine period:

πn \leq x < π + πn

and undefined points.

The domain is

πn < x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

f (x) = - 2 0^{2} + 360 x + 1000

\frac{16 x ^{2} - 49}{x ^{2} - 64}

\frac{2 x ^{5} - 3}{x ^{5} - 1}

y = \frac{2 x + 2}{x + 2}

y = - \frac{2 x + 2}{x ^{2} - 1}

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