Show that the functions f1(x) = x 1, if x 1, 2(x 1), if x < 1, f2(x) = 2x, f3(x) = 3

Chapter 4, Problem 42

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Show that the functions f1(x) = x 1, if x 1, 2(x 1), if x < 1, f2(x) = 2x, f3(x) = 3 form a linearly independent set on (,). Determine all intervals on which { f1, f2, f3} is linearly dependent.

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