Let f(x) be a continuous function defined on [0,1] that satisfies f(0)<0 and f(1)>0. Let c ∈ R, and consider the function g(x) = f(x) + c(1 − 2x). Find all possible values of c ∈ R for which you can guarantee that there exists an x ∈ [0, 1] such that g(x) = 0. Hint: Considerthecasesc<0,c=0,andc>0.

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