Practice Surjective Functions (24.1.3) - Functions - Discrete Mathematics - Vol 1
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Surjective Functions

Practice - Surjective Functions

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Learning

Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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?

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

Prove the non-surjectiveness of f(x) = sqrt(x) over integers to integers.

💡 Hint: Consider outputs possible given the input constraints you set.

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