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Mathematics
Problem
Determine the domain of
f
(
x
)
=
sec
(
2
x
−
π
3
)
f(x)=\sec\!\left(2x-\dfrac{\pi}{3}\right)
f
(
x
)
=
sec
(
2
x
−
3
π
)
. a)
R
∖
{
x
=
π
6
+
n
π
2
,
n
∈
Z
}
\mathbb{R}\setminus\left\{x=\dfrac{\pi}{6}+\dfrac{n\pi}{2},\;n\in\mathbb{Z}\right\}
R
∖
{
x
=
6
π
+
2
nπ
,
n
∈
Z
}
b)
R
∖
{
x
=
π
3
+
n
π
2
,
n
∈
Z
}
\mathbb{R}\setminus\left\{x=\dfrac{\pi}{3}+\dfrac{n\pi}{2},\;n\in\mathbb{Z}\right\}
R
∖
{
x
=
3
π
+
2
nπ
,
n
∈
Z
}
c)
R
∖
{
x
=
5
π
12
+
n
π
2
,
n
∈
Z
}
\mathbb{R}\setminus\left\{x=\dfrac{5\pi}{12}+\dfrac{n\pi}{2},\;n\in\mathbb{Z}\right\}
R
∖
{
x
=
12
5
π
+
2
nπ
,
n
∈
Z
}
d)
R
∖
{
x
=
π
6
+
n
π
,
n
∈
Z
}
\mathbb{R}\setminus\left\{x=\dfrac{\pi}{6}+n\pi,\;n\in\mathbb{Z}\right\}
R
∖
{
x
=
6
π
+
nπ
,
n
∈
Z
}
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