What is the domain of f(x)=3csc(6x)+8 ?

The domain of f(x)=3csc(6x)+8 is pi/3 n<x< pi/6+pi/3 n\lor pi/6+pi/3 n<x< pi/3+pi/3 n

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domain of f(x)=3csc(6x)+8

domain

f (x) = 3 csc (6 x) + 8

\frac{π}{3} n < x < \frac{π}{6} + \frac{π}{3} n or \frac{π}{6} + \frac{π}{3} n < x < \frac{π}{3} + \frac{π}{3} n

Interval Notation

(\frac{π}{3} n, \frac{π}{6} + \frac{π}{3} n) \cup (\frac{π}{6} + \frac{π}{3} n, \frac{π}{3} + \frac{π}{3} n)

Solution steps

Take the denominator(s) of

3 csc (6 x) + 8

and compare to zero:

x = \frac{π}{3} n, x = \frac{π}{6} + \frac{π}{3} n

Periodicity of

3 csc (6 x) + 8 : \frac{π}{3}

Combine period:

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

and undefined points.

The domain is

\frac{π}{3} n < x < \frac{π}{6} + \frac{π}{3} n or \frac{π}{6} + \frac{π}{3} n < x < \frac{π}{3} + \frac{π}{3} n

What is the domain of f(x)=3csc(6x)+8 ?
The domain of f(x)=3csc(6x)+8 is pi/3 n<x< pi/6+pi/3 n\lor pi/6+pi/3 n<x< pi/3+pi/3 n