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

The domain of y=2sec(3x-pi)+1 is

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

domain

y = 2 sec (3 x - π) + 1

\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

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

2 sec (3 x - π) + 1

and compare to zero:

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

Periodicity of

2 sec (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 \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

y = (x + 2)^{2}

f (x) = 22 x - 1694 = 0

f (x) = arctan (\frac{1}{x + 1})

p (x) = 25 - 3 x

(x - 6) - (x + 2)