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Mathematics
Problem
Consider
f
:
(
0
,
∞
)
→
(
−
π
2
,
π
2
)
f:(0,\infty)\to\left(-\frac{\pi}{2},\frac{\pi}{2}\right)
f
:
(
0
,
∞
)
→
(
−
2
π
,
2
π
)
, defined as
f
(
x
)
=
tan
−
1
(
log
e
x
(
log
e
x
)
2
+
1
)
.
f(x)=\tan^{-1}\left(\frac{\log_e x}{(\log_e x)^2+1}\right).
f
(
x
)
=
tan
−
1
(
(
lo
g
e
x
)
2
+
1
lo
g
e
x
)
.
The above function can be classified as a. Injective but not surjective b. Surjective but not bijective c. Neither injective nor surjective d. Both injective and surjective
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