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Range of values

Source: China Southeast Math Olympiad 2015 Day 2 P5

June 6, 2017
algebra

Problem Statement

Suppose that a,ba,b are real numbers, function f(x)=ax+bf(x) = ax+b satisfies ∣f(x)∣≤1\mid f(x) \mid \leq 1 for any x∈[0,1]x \in [0,1]. Find the range of values of S=(a+1)(b+1).S= (a+1)(b+1).
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