Practice Injective Functions (24.1.2) - Functions - Discrete Mathematics

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6 sample questions

Question 1.
What is an injective function?
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Think about what happens if two inputs give the same output.
Question 2.
Is the function f(x) = 2x injective?
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You can test with any two different x values.
3Question 3.
Which of the following is true about injective functions?
- f(a) = f(b) implies a = b
- f(a) = f(b) can imply a ≠ b
- f(a) can have multiple values for b
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Remember about the unique mapping quality.
4Question 4.
Is the function f(x) = x² an injective function over the reals?
- True
- False
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Consider different values that yield the same result.
Question 5.
Demonstrate that the function f(x) = x^3 is injective over the real numbers.
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Consider the properties of cubic functions.
Question 6.
If a function f: A → B is injective, what can be said about its inverse f^−1: B → A?
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Reflect on how injections relate to inverses.

5 more questions in this section. Enroll free to practise them all.