query: Prove $f(x)=x^3+x$ is injective
positive_passages.docid: 19355
positive_passages.text: prove $f(x)=x^3+x$ is one to one and onto
negative_passages.docid: 102553
negative_passages.text: How to show that $f(z) = f(i)$
negative_passages.docid: 144601
negative_passages.text: Given $f(x+T) = f(x) + a$, prove that $f(x) = \varphi(x) + {a \over T}x$, where $\varphi(x)$ is periodic with period $T$
negative_passages.docid: 48592
negative_passages.text: Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists
negative_passages.docid: 126427
negative_passages.text: Proving $\sqrt{2}+\sqrt[3]{3}$ is algebraic.
negative_passages.docid: 104949
negative_passages.text: How would I prove that this function is affine if $f(x+h)-f(x)=hf'(x)$?
negative_passages.docid: 115636
negative_passages.text: Show that $f$ is either injective or a constant function.
negative_passages.docid: 66772
negative_passages.text: $f(f(x)f(y))+f(x+y)=f(xy)$
negative_passages.docid: 64866
negative_passages.text: Proving a Composition of Functions is Bijective
negative_passages.docid: 121395
negative_passages.text: 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.
negative_passages.docid: 93102
negative_passages.text: prove that $f:X\rightarrow Y$ is surjective if and only if $f(f^{-1}(C))=C$
negative_passages.docid: 72644
negative_passages.text: Continuous injective map $f:\mathbb{R}^3 \to \mathbb{R}$?
negative_passages.docid: 17310
negative_passages.text: Can $f(x)=|x|^3$ be differentiated
negative_passages.docid: 72251
negative_passages.text: $g\circ f$ is Surjective and $g$ is Injective then Prove that $f$ is surjective
negative_passages.docid: 134043
negative_passages.text: Prove that for $ f(x+2\cdot\pi)=f(x), x \in \mathbb{R} $, there exists $ x_0 $ so $ f(x_0+\pi)=f(x_0) $
negative_passages.docid: 65977
negative_passages.text: Showing function is injective iff $f(M_1 \cap M_2) = f(M_1)\cap f(M_2)$
negative_passages.docid: 113359
negative_passages.text: Proving that $x^2 + 4$ is not divisible by $3$