If $f$ is injective, show that the function $g : A \rightarrow f(A)$ is bijective where $g(a) = f(a)$ for each $a \in A$.
29769
Can I make any injective function bijective by patching the codomain?
157756
Examine if function $f:\mathbb{R^2}\rightarrow \mathbb{R^2}$ which is defined as $f(x,y)=(2x-y,x-4y)$ is bijective. If bijective, find $f^{-1}$.
10307
Show the inverse of a bijective function is bijective
1371
Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.
121395
Let $X$ and $Y$ be non-empty sets and let $f:X \rightarrow Y$. Prove that $ f^{ −1} :P(Y ) → P(X) $ is injective if, and only if, $f$ is surjective.
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
21891
If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
53168
Surjective, Injective, Bijective Functions from $\mathbb Z$ to itself
28692
Find if set $I$ of all injective functions $\mathbb{N} \rightarrow \mathbb{N}$ is equinumerous to $\mathbb{R}$
157268
Proving a bijection with absolute value
53971
If $g:V \rightarrow V$ is an injective linear transformation. Prove if $V$ is finite dimensional then $g$ is surjective.
60348
How do I prove $F(a)=F(a^2)?$
47135
Prove if a = b, then f(a) = f(b) for any function f (with natural deduction)
76674
Let $S:U\rightarrow V, \ T:V\rightarrow W$ and if $S$ and $T$ are both injective/surjective, is $T\circ S$ injective/surjective?
85768
The function $f:G \rightarrow G$ defined by $f(x)=x^2$ is a homomorphism iff G is abelian.
22061
$|f(x)-f(y)|\geq k|x-y|$.Then $f$ is bijective and its inverse is continuous.