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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define surjective function.
💡 Hint: Think about how outputs relate to inputs.
Question 2
Easy
Is f(x) = x^2: ℤ -> ℤ+ surjective? Explain.
💡 Hint: Consider the potential outputs when inputs are negative.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
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
💡 Hint: Think about the purpose of a surjective function.
Question 2
True or False: The function f(x) = sin(x) from R to R is surjective.
- True
- False
💡 Hint: What are the limits of the sine function?
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Design a surjective function from ℝ to ℝ and prove it remains surjective under defined conditions.
💡 Hint: Define mappings for both linear and nonlinear functions in real number domains.
Question 2
Prove the non-surjectiveness of f(x) = sqrt(x) over integers to integers.
💡 Hint: Consider outputs possible given the input constraints you set.
Challenge and get performance evaluation