What is the domain of sec(x) ?

The domain of sec(x) is 2pin<= x< pi/2+2pin\lor pi/2+2pin<x<(3pi)/2+2pin\lor (3pi)/2+2pin<x<2pi+2pin

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domain of sec(x)

domain

sec (x)

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

Interval Notation

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

Solution steps

Take the denominator(s) of

sec (x)

and compare to zero:

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

Periodicity of

sec (x) : 2 π

Combine period:

2 πn \leq x < 2 π + 2 πn

and undefined points.

The domain is

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

f (x) = x^{3} + 6 x^{2} + 16

(- 10, 3), (2, 8)

\frac{4}{x ^{2} - 1}

f (x) = \frac{2 x ^{4} + 5 x + 5}{5 x ^{4} + 4 x - 2}

\frac{x ^{3} + 3}{x}

What is the domain of sec(x) ?
The domain of sec(x) is 2pin<= x< pi/2+2pin\lor pi/2+2pin<x<(3pi)/2+2pin\lor (3pi)/2+2pin<x<2pi+2pin