What is the domain of y=2csc(3x-pi)+1 ?

The domain of y=2csc(3x-pi)+1 is (2pi)/3 n<x< pi/3+(2pi)/3 n\lor pi/3+(2pi)/3 n<x<(2pi)/3+(2pi)/3 n

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domain of y=2csc(3x-pi)+1

domain

\frac{2 π}{3} n < x < \frac{π}{3} + \frac{2 π}{3} n or \frac{π}{3} + \frac{2 π}{3} n < x < \frac{2 π}{3} + \frac{2 π}{3} n

Interval Notation

(\frac{2 π}{3} n, \frac{π}{3} + \frac{2 π}{3} n) \cup (\frac{π}{3} + \frac{2 π}{3} n, \frac{2 π}{3} + \frac{2 π}{3} n)

Solution steps

Take the denominator(s) of

2 csc (3 x - π) + 1

and compare to zero:

x = \frac{π}{3} + \frac{2 π}{3} n, x = \frac{2 π}{3} n

Periodicity of

2 csc (3 x - π) + 1 : \frac{2 π}{3}

Combine period:

\frac{2 π}{3} n \leq x < \frac{2 π}{3} + \frac{2 π}{3} n

and undefined points.

The domain is

\frac{2 π}{3} n < x < \frac{π}{3} + \frac{2 π}{3} n or \frac{π}{3} + \frac{2 π}{3} n < x < \frac{2 π}{3} + \frac{2 π}{3} n

What is the domain of y=2csc(3x-pi)+1 ?
The domain of y=2csc(3x-pi)+1 is (2pi)/3 n<x< pi/3+(2pi)/3 n\lor pi/3+(2pi)/3 n<x<(2pi)/3+(2pi)/3 n