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Problem
Problem
Let
f
:
(
−
1
,
1
)
→
B
f: (-1, 1) \rightarrow B
f
:
(
−
1
,
1
)
→
B
, be a function defined by
f
(
x
)
=
tan
−
1
2
x
1
−
x
2
f(x) = \tan^{-1} \frac{2x}{1-x^2}
f
(
x
)
=
tan
−
1
1
−
x
2
2
x
, then
f
f
f
is both one-one and onto when
B
B
B
is the interval (a)
[
−
π
2
,
π
2
]
\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]
[
−
2
π
,
2
π
]
(b)
(
−
π
2
,
π
2
)
\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)
(
−
2
π
,
2
π
)
(c)
(
0
,
π
2
)
\left(0, \frac{\pi}{2}\right)
(
0
,
2
π
)
(d)
[
0
,
π
2
)
\left[0, \frac{\pi}{2}\right)
[
0
,
2
π
)
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