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Mathematics
Mathematics
Problem
If the range of function
f
(
x
)
=
(
π
2
+
cos
−
1
α
)
x
2
+
2
(
cos
−
1
β
)
x
+
π
2
−
cos
−
1
α
f(x) = (\pi\sqrt{2} + \cos^{-1}\alpha)x^2 + 2(\cos^{-1}\beta)x + \pi\sqrt{2} - \cos^{-1}\alpha
f
(
x
)
=
(
π
2
+
cos
−
1
α
)
x
2
+
2
(
cos
−
1
β
)
x
+
π
2
−
cos
−
1
α
is
[
0
,
∞
)
[0, \infty)
[
0
,
∞
)
then find the value of
∣
α
−
β
∣
+
2
α
β
+
1
|\alpha - \beta| + 2\alpha\beta + 1
∣
α
−
β
∣
+
2
α
β
+
1
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