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12
trinomial, f(\sqrt2)=3, |f(x)| < 1 for all x \in [-1, 1] (HOMC 2013 Q12)
trinomial, f(\sqrt2)=3, |f(x)| < 1 for all x \in [-1, 1] (HOMC 2013 Q12)
Source:
August 1, 2019
algebra
quadratic function
Problem Statement
The function
f
(
x
)
=
a
x
2
+
b
x
+
c
f(x) = ax^2 + bx + c
f
(
x
)
=
a
x
2
+
b
x
+
c
satisfies the following conditions:
f
(
2
)
=
3
f(\sqrt2)=3
f
(
2
)
=
3
and
∣
f
(
x
)
∣
≤
1
|f(x)| \le 1
∣
f
(
x
)
∣
≤
1
for all
x
∈
[
−
1
,
1
]
x \in [-1, 1]
x
∈
[
−
1
,
1
]
. Evaluate the value of
f
(
2013
)
f(\sqrt{2013})
f
(
2013
)
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