Q1. Claim: Suppose f : R(adsbygoogle = window.adsbygoogle || []).push({}); ^{n}-> R^{m}is injective. Then m >= n. Is this true?

Q2. Claim: Suppose f : R^{n}-> R^{n}is injective and f(X) = [f_{1}(X) f_{2}(X) ... f_{n}(X)]^{T}. Then each f_{k}must be injective. Is this true?

Q3. I assume the above claims are known results or have known counterexamples. Can someone direct me to a good text or reference for questions such as these?

Thanks.

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# Three questions on injective functions.

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