mth 103 blueprint Marked out of 1.00 Flag question A function \( f \) is said to be bijective if it is Select one: Surjective Injective Injective and surjective discontinuous Continuous Previous page Next page Scanned by CamScanner Question 7
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A function \( f \) is bijective if it is both injective (one-to-one) and surjective (onto). Show more…
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a) Find an example of an injective function f: A -> B and a surjective function g: B -> C such that g o f: A -> C is neither injective nor surjective. b) Decide if the following functions from R to R are injective, surjective, or bijective: f(x) = 2x + 5, f(x) = x^6 - 2, f(x) = 2*sqrt(x). c) For the following functions, determine whether they are injective, surjective, or bijective: a) f: [0, ) -> R given by f(x) = tan(x) b) f: [0,1) x (0,7/3) -> [0,1) given by f(r,θ) = r cos(θ).
Joseph D.
Which of the following is a synonym for a one-to-one function? bijection surjection injection rejection Question 2 Which of the following is true about the above arrow diagram? It properly defines a function but it is not a one-to-one function It properly defines a function but it is not onto It does not define a function because 3 is not mapped to any element of B It does not define a function because y is not mapped to by any element of A Question 3 Consider the function f: ℤ → ℤ, where f(n) = 2n + 1. Which of the following correctly describe domain, codomain and range? The domain and codomain are the set of all integers, but the range includes only the odd integers The domain, codomain, and range are the set of all integers The domain and range are the set of all integers, but the codomain includes only the odd integers The domain and range are the set of all integers, but the codomain includes only the even integers Question 4 Which of the following functions is a one-to-one function? f: ℤ → ℤ, where f(n) = |2n - 1| f: ℝ → ℝ, where f(x) = 3x² + 6 f: ℝ → ℝ, where f(x) = 2x + 7 f: ℤ → ℤ, where f(n) = |n| - 7 Question 5 Which of the following functions is an onto function? f: ℝ → ℝ, where f(x) = 3x + 5 f: ℤ → ℤ, where f(n) = |n - 1| f: ℝ → ℝ, where f(x) = 3x² + 6 f: ℤ → ℤ, where f(n) = 6n - 7
Adi S.
6. Let g : A → B and h : B → C be functions (a) If g and h are both injective, show that h ∘ g is also injective. (b) If g and h are both surjective, show that h ∘ g is also surjective. (c) If g and h are both bijective, deduce that h ∘ g is also bijective, and show that (h ∘ g)⁻¹ = g⁻¹ ∘ h⁻¹.
Shyam P.
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