Practice Part (c): Injectivity Of G (2.6.3) - Introduction - Discrete Mathematics

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6 sample questions

Question 1.
What does it mean for a function to be injective?
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Think about one-to-one relationships.
Question 2.
Is the function f(x) = x^2 injective over the real numbers?
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Check distinct inputs leading to the same output.
3Question 3.
What guarantees a function to be injective?
- Unique output for each input
- Multiple outputs for one input
- Every output is covered
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Define injectivity clearly.
4Question 4.
If g∘f is injective, does that imply g is injective?
- True
- False
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Consider the definitions discussed.
Question 5.
Given two functions f(x) = x + 2 and g(x) = x^2, discuss and prove if g∘f is injective.
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Analyze the composition step by step.
Question 6.
Construct a real-world situation illustrating a surjective function that fails to be injective.
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Think of various qualifications leading to common roles.

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