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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does it mean for a function to be injective?
💡 Hint: Think about one-to-one relationships.
Question 2
Easy
Is the function f(x) = x^2 injective over the real numbers?
💡 Hint: Check distinct inputs leading to the same output.
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 guarantees a function to be injective?
- Unique output for each input
- Multiple outputs for one input
- Every output is covered
💡 Hint: Define injectivity clearly.
Question 2
If g∘f is injective, does that imply g is injective?
- True
- False
💡 Hint: Consider the definitions discussed.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given two functions f(x) = x + 2 and g(x) = x^2, discuss and prove if g∘f is injective.
💡 Hint: Analyze the composition step by step.
Question 2
Construct a real-world situation illustrating a surjective function that fails to be injective.
💡 Hint: Think of various qualifications leading to common roles.
Challenge and get performance evaluation