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Mathematics
Mathematics
Problem
The largest interval lying in
(
−
π
2
,
π
2
)
\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)
(
−
2
π
,
2
π
)
for which the function,
f
(
x
)
=
4
−
x
2
+
cos
−
1
(
x
2
−
1
)
+
log
(
cos
x
)
f(x) = 4^{-x^2} + \cos^{-1}\left(\frac{x}{2} - 1\right) + \log(\cos x)
f
(
x
)
=
4
−
x
2
+
cos
−
1
(
2
x
−
1
)
+
lo
g
(
cos
x
)
, is defined, is [2007] (a)
[
−
π
4
,
π
2
)
\left[-\frac{\pi}{4}, \frac{\pi}{2}\right)
[
−
4
π
,
2
π
)
(b)
[
0
,
π
2
)
\left[0, \frac{\pi}{2}\right)
[
0
,
2
π
)
(c)
[
0
,
π
]
[0, \pi]
[
0
,
π
]
(d)
(
−
π
2
,
π
2
)
\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)
(
−
2
π
,
2
π
)
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