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Question:

Let A = {x ∈ R: x is not a positive integer}. Define a function f: A → R as f(x) = 2x. Then f is:

not injective

surjective but not injective

neither injective nor surjective

injective but not surjective

Solution:

f(x) = 2(1 + 1/x)
f'(x) = -2/x²
⇒ f is one-one but not onto