Lecture 1 - UH

Examples and Counter-Examples Examples 3. • f(x) = 3x−5 is 1-to-1. • f(x) = x2 is not 1-to-1. • f(x) = x3 is 1-to-1. • f(x) = 1 x is 1-to-1. • f(x) = xn −x, n > 0, is not 1-to-1. Proof. • f(x 1) = f(x 2) ⇒ 3x 1 − 5 = 3x 2 − 5 ⇒ x 1 = x 2.In general, f(x) = ax−b, a 6= 0, is 1-to-1.

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