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"Consider a function, f : Z → Z where f(x) = 3x + 3

(a) Prove or disprove whether f is injective

User Stoyan
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Final answer:

A function is injective if each element in the domain is paired with a unique element in the codomain. The given function f(x) = 3x + 3 is injective because for any two different values of x, the output will be different.

Step-by-step explanation:

A function is injective or one-to-one if each element in the domain is paired with a unique element in the codomain. To prove or disprove whether f(x) = 3x + 3 is injective, we need to show if there are any two different values of x that produce the same output. Let's assume f(x1) = f(x2) and try to simplify the equation: 3x1 + 3 = 3x2 + 3. By subtracting 3 from both sides and dividing by 3, we get x1 = x2. This indicates that the function is indeed injective because for any two different values of x, the output will be different.

User Evan Ward
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