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Suppose that g ◦ f is surjective. Let z ∈ C. Then since g ◦ f is surjective, there exists x ∈ A such that (g ◦ f)(x) = g(f(x)) = z. Therefore if we let y = f(x) ∈ B, then g(y) = z. Thus g is surjective.

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Pooja Khatri asked Apr 11, 2019
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Let $a$ and $b$ be real numbers with $a<b$. Use the floor and / or ceiling functions to express the number of integers $n$ that satisfy the inequality $a<n<b.$