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Mathematics
Mathematics
Problem
Consider the function
f
(
x
)
=
a
tan
(
2
x
)
+
b
f(x)=a\tan(2x)+b
f
(
x
)
=
a
tan
(
2
x
)
+
b
, where
x
≠
(
2
n
+
1
)
π
4
x\neq\frac{(2n+1)\pi}{4}
x
=
4
(
2
n
+
1
)
π
,
n
∈
Z
n\in\mathbb{Z}
n
∈
Z
and
a
,
b
∈
R
a,b\in\mathbb{R}
a
,
b
∈
R
. The graph of
y
=
f
(
x
)
y=f(x)
y
=
f
(
x
)
passes through the points
(
π
12
,
5
)
\left(\frac{\pi}{12},5\right)
(
12
π
,
5
)
and
(
π
3
,
7
)
\left(\frac{\pi}{3},7\right)
(
3
π
,
7
)
. a. Write down the period of
f
f
f
. b. Find the value of
a
a
a
and the value of
b
b
b
.
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