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Alsosaid1987 (talk | contribs) Added info on specialized arrows for injective function to match analogous information in the corresponding surjective function article. |
m →Examples: Linkify first occurence of 'surjective' |
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* The function <math>f : \R \to \R</math> defined by <math>f(x) = 2 x + 1</math> is injective.
* The function <math>g : \R \to \R</math> defined by <math>g(x) = x^2</math> is {{em|not}} injective, because (for example) <math>g(1) = 1 = g(-1).</math> However, if <math>g</math> is redefined so that its ___domain is the non-negative real numbers <nowiki>[0,+∞)</nowiki>, then <math>g</math> is injective.
* The [[exponential function]] <math>\exp : \R \to \R</math> defined by <math>\exp(x) = e^x</math> is injective (but not [[Surjective function|surjective]], as no real value maps to a negative number).
* The [[natural logarithm]] function <math>\ln : (0, \infty) \to \R</math> defined by <math>x \mapsto \ln x</math> is injective.
* The function <math>g : \R \to \R</math> defined by <math>g(x) = x^n - x</math> is not injective, since, for example, <math>g(0) = g(1) = 0.</math>
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