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f(2x - x^2) increasing if f(t) increasing in -8 \le t \le 8

Source: Spanish Mathematical Olympiad 1967 P1

December 4, 2022
algebraanalysis

Problem Statement

It is known that the real function f(t)f(t) is monotonic increasing in the interval −8≤t≤8-8 \le t \le 8, but nothing is known about what happens outside of it. In what range of values of xx, can it be ensured that the function y=f(2x−x2)y = f(2x - x^2) is monotonic increasing?
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