Practice One-to-one Function (injective Function) (2.2.1)

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6 sample questions

Question 1.
Identify if the function f(x) = 3x + 1 is injective. Why?
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Consider what happens with different x-values.
Question 2.
What is the definition of an injective function?
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Think about what injective means in terms of pairs.
3Question 3.
What is an injective function?
- A function where every output has a unique input.
- A function that is surjective.
- A function with no restrictions.
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Think about unique mappings.
4Question 4.
True or False: If f(a) = f(b) for a function f, then a = b.
- True
- False
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Consider what happens with injective functions.
Question 5.
Prove whether the function g(x) = 4x - 5 is injective and explain your reasoning.
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Use algebraic manipulation to explore.
Question 6.
Consider the function h(x) = sin(2x). Is it injective over the interval [0, π] and why?
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Assess the behavior of sine over the interval.

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