Practice Surjective Functions (24.1.3) - Functions - Discrete Mathematics

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6 sample questions

Question 1.
Define surjective function.
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Think about how outputs relate to inputs.
Question 2.
Is f(x) = x^2: ℤ -> ℤ+ surjective? Explain.
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Consider the potential outputs when inputs are negative.
3Question 3.
What must be true for a function to be considered surjective?
- Every element has multiple pre-images
- Every element in the co-domain has at least one pre-image
- No element in the co-domain can be mapped
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Think about the purpose of a surjective function.
4Question 4.
True or False: The function f(x) = sin(x) from R to R is surjective.
- True
- False
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What are the limits of the sine function?
Question 5.
Design a surjective function from ℝ to ℝ and prove it remains surjective under defined conditions.
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Define mappings for both linear and nonlinear functions in real number domains.
Question 6.
Prove the non-surjectiveness of f(x) = sqrt(x) over integers to integers.
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Consider outputs possible given the input constraints you set.

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