Prove that if the real-valued function f is strictly increasing, then f is oneto-one.

Question

Mathematics

Salma Acevedo

27 June, 16:01

Prove that if the real-valued function f is strictly increasing, then f is oneto-one.

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Answers (1)

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Tate Townsend · Answer 1

See proof below

Step-by-step explanation:

Let x, y be arbitrary real numbers. We want to prove that if x≠y then f (x) ≠f (y) (this is the definition of 1-1).

If x≠y, we can assume, without loss of generality that x
Because f is strictly increasing, x