If $g \circ f$ is surjective, what can you say about the surjectivity of $f$ and $g$?
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What can you say about $f$ and $g$ in the case that $fg$ is 1) Injective, 2) Surjective - Cohn - Classic Algebra Page 15
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Prove composition of two surjections is surjection
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Show there exists $g:(0,1)\to\mathbb{R}^2$ such that $h\circ g$ constant, $g$ continuously differentiable and $g$ injective
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If $g \circ f$ is the identity function, then which of $f$ and $g$ is onto and which is one-to-one?
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Let $f:K\to K$ with $\|f(x)-f(y)\|\geq ||x-y||$ for all $x,y$. Show that equality holds and that $f$ is surjective.
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Does a surjective ring homomorphism have to be surjective on the unit groups?
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A continuous bijection $f:\mathbb{R}\to \mathbb{R}$ is an homeomorphism?
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Let functions $ f: A \to B$ and $g: B \to A$, suppose that $ g \circ f = i_A$. Prove that if $f$ is onto, then $g$ is one-to-one
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Show that if $g \circ f$ is injective, then so is $f$.
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If $g \circ f$ is injective, so is $g$
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If $L:\mathbb{R}^n \rightarrow \mathbb{R}^m$ and $m<n$ linear trans. What does this tell about injectivity and surjectivity?
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Example of $f,g: [0,1]\to[0,1]$ and Riemann-integrable, but $g\circ f$ is not?
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Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
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Example where $f\circ g$ is bijective, but neither $f$ nor $g$ is bijective
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Prove that rank $(g \circ f)\le \min[\operatorname{rank}(f),\operatorname{rank}(g)]$; $g$ and $f$ are linear mappings
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Constructing a Bijective function via an injective and surjective one.
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Proving that a continuous map is surjective