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Popular >

domain of sec(3x)

Solution

domain

sec (3 x)

Solution

\frac{2 π}{3} n \leq x < \frac{π}{6} + \frac{2 π}{3} n or \frac{π}{6} + \frac{2 π}{3} n < x < \frac{π}{2} + \frac{2 π}{3} n or \frac{π}{2} + \frac{2 π}{3} n < x < \frac{2 π}{3} + \frac{2 π}{3} n

+1

Interval Notation

[\frac{2 π}{3} n, \frac{π}{6} + \frac{2 π}{3} n) \cup (\frac{π}{6} + \frac{2 π}{3} n, \frac{π}{2} + \frac{2 π}{3} n) \cup (\frac{π}{2} + \frac{2 π}{3} n, \frac{2 π}{3} + \frac{2 π}{3} n)

Solution steps

Take the denominator(s) of

sec (3 x)

and compare to zero:

x = \frac{π}{6} + \frac{2 π}{3} n, x = \frac{π}{2} + \frac{2 π}{3} n

Periodicity of

sec (3 x) : \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 \leq x < \frac{π}{6} + \frac{2 π}{3} n or \frac{π}{6} + \frac{2 π}{3} n < x < \frac{π}{2} + \frac{2 π}{3} n or \frac{π}{2} + \frac{2 π}{3} n < x < \frac{2 π}{3} + \frac{2 π}{3} n

Popular Examples

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f (x) = \frac{1}{ln ( x )}

Frequently Asked Questions (FAQ)

What is the domain of sec(3x) ?
The domain of sec(3x) is