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

The domain of 3csc(3x+pi)-2 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 3csc(3x+pi)-2

domain

3 csc (3 x + π) - 2

\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

3 csc (3 x + π) - 2

and compare to zero:

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

Periodicity of

3 csc (3 x + π) - 2 : \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

ln (- x^{2} + 5 x + 2)

f (x) = lo g_{5} (x - 4) + 2

\frac{30000}{100 - x}

arcsin (5 x - 1)

f (x) = \frac{x ^{2} - 1}{x ^{2} + 1}

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