Let f: R → R be given by f (x) = (x − 1)². Prove that f(x) is neither one-to-one nor onto.

Database System Concepts
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ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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6. Let ƒ : R → R be given by ƒ (x) = (x − 1)². Prove that f (x) is neither one-to-one nor onto..
Transcribed Image Text:6. Let ƒ : R → R be given by ƒ (x) = (x − 1)². Prove that f (x) is neither one-to-one nor onto..
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Step 1

Suppose x1 and x2 are real numbers such that f(x1) = f(x2). (We need to show x1  x2).

x1 - 12 = x2 - 12x1 - 1 = x2 - 1 ORx1 - 1 = 1 - x2

There are two possible values for x1x2 and 2 - x2.

Since the value for x1 can be two different values, f(x) is not one-to-one.

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