Practice - Part (c): Injectivity of g
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Practice Questions
Test your understanding with targeted questions
What does it mean for a function to be injective?
💡 Hint: Think about one-to-one relationships.
Is the function f(x) = x^2 injective over the real numbers?
💡 Hint: Check distinct inputs leading to the same output.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What guarantees a function to be injective?
💡 Hint: Define injectivity clearly.
If g∘f is injective, does that imply g is injective?
💡 Hint: Consider the definitions discussed.
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Challenge Problems
Push your limits with advanced challenges
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.
Construct a real-world situation illustrating a surjective function that fails to be injective.
💡 Hint: Think of various qualifications leading to common roles.
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