If ƒ : Z → {0, 1, 2} is a function which is not surjective, which of the following statements is necessarily true? For all k = {0, 1, 2} we have |ƒ−¹(k)| > 0. For all k = {0, 1, 2} we have |ƒ−¹(k)| = ∞. There is at least one k = {0, 1, 2} such that |ƒ-¹(k)| = ∞, and at least one k = {0, 1, 2} such that f-¹(k)| = 0. The function f cannot exist as |Z| = ∞ and |{0, 1, 2}| = 3.
If ƒ : Z → {0, 1, 2} is a function which is not surjective, which of the following statements is necessarily true? For all k = {0, 1, 2} we have |ƒ−¹(k)| > 0. For all k = {0, 1, 2} we have |ƒ−¹(k)| = ∞. There is at least one k = {0, 1, 2} such that |ƒ-¹(k)| = ∞, and at least one k = {0, 1, 2} such that f-¹(k)| = 0. The function f cannot exist as |Z| = ∞ and |{0, 1, 2}| = 3.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Transcribed Image Text:If ƒ : Z → {0, 1, 2} is a function which is not surjective, which of the following
statements is necessarily true?
For all k = {0, 1, 2} we have |ƒ¯¹(k)| > 0.
O For all k = {0, 1, 2} we have |ƒ-¹(k)| = ∞.
-1
O There is at least one k = {0, 1, 2} such that |ƒ¯¹(k)| = ∞, and at least one k = {0, 1, 2} such
that |ƒ−¹(k)| = 0.
The function f cannot exist as |Z| = ∞ and {0, 1, 2}| = 3.
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