Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Exercise 3. Is there a number that is exactly one less than its fifth power? DEFINITION 3 (INJECTIVE FUNCTION). Let A, B C R be two subsets of the real numbers, and let f : A → B be a function. We say that f is injective (we might alternatively say that f is 1-to-1) if for all a₁, a2 € A such that f(a₁) = f(a₂) we have that a₁ = a2. DEFINITION 4 (SURJECTIVE FUNCTION). Let A, B C R be two subsets of the real numbers, and let f : A → B be a function. We say that f is surjective (we might alternatively say that f is onto) if for every b = B we can find a € A such that f(a) = b.
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Transcribed Image Text:Exercise 3. Is there a number that is exactly one less than its fifth power? DEFINITION 3 (INJECTIVE FUNCTION). Let A, B C R be two subsets of the real numbers, and let f : A → B be a function. We say that f is injective (we might alternatively say that f is 1-to-1) if for all a₁, a2 € A such that f(a₁) = f(a₂) we have that a₁ = a2. DEFINITION 4 (SURJECTIVE FUNCTION). Let A, B C R be two subsets of the real numbers, and let f : A → B be a function. We say that f is surjective (we might alternatively say that f is onto) if for every b = B we can find a € A such that f(a) = b.
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