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Problem
Problem
If the mapping
f
(
x
)
=
a
x
+
b
f(x) = ax + b
f
(
x
)
=
a
x
+
b
,
a
<
0
a < 0
a
<
0
and maps
[
−
1
,
1
]
[-1, 1]
[
−
1
,
1
]
onto
[
0
,
2
]
[0, 2]
[
0
,
2
]
, then for all values of
θ
\theta
θ
,
A
=
cos
2
θ
+
sin
4
θ
A = \cos^2 \theta + \sin^4 \theta
A
=
cos
2
θ
+
sin
4
θ
is such that a.
f
(
1
4
)
≤
A
≤
f
(
0
)
f\left(\frac{1}{4}\right) \le A \le f(0)
f
(
4
1
)
≤
A
≤
f
(
0
)
b.
f
(
0
)
≤
A
≤
f
(
−
2
)
f(0) \le A \le f(-2)
f
(
0
)
≤
A
≤
f
(
−
2
)
c.
f
(
1
3
)
≤
A
≤
f
(
0
)
f\left(\frac{1}{3}\right) \le A \le f(0)
f
(
3
1
)
≤
A
≤
f
(
0
)
d.
f
(
−
1
)
<
A
≤
f
(
−
2
)
f(-1) < A \le f(-2)
f
(
−
1
)
<
A
≤
f
(
−
2
)
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