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Spain Mathematical Olympiad
1967 Spain Mathematical Olympiad
1
1
Part of
1967 Spain Mathematical Olympiad
Problems
(1)
f(2x - x^2) increasing if f(t) increasing in -8 \le t \le 8
Source: Spanish Mathematical Olympiad 1967 P1
12/4/2022
It is known that the real function
f
(
t
)
f(t)
f
(
t
)
is monotonic increasing in the interval
−
8
≤
t
≤
8
-8 \le t \le 8
−
8
≤
t
≤
8
, but nothing is known about what happens outside of it. In what range of values of
x
x
x
, can it be ensured that the function
y
=
f
(
2
x
−
x
2
)
y = f(2x - x^2)
y
=
f
(
2
x
−
x
2
)
is monotonic increasing?
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