$|f(x)g(x)| = |(f(x)||g(x)|$
118592
Prove that the absolute value of a product is the product of the absolute values of factors.
14277
Proving $f(x)=x\cdot |x|$ is a bijection
107659
Let $f:A \to B$ and $g:B\to A$ be arbitrary functions.
106830
are $f(f(x))=f(x)$ and $f(x)=x$ equivalent?
32575
What's the name for the property of a function $f$ that means $f(f(x))=x$?
13253
Prove $f(S \cup T) = f(S) \cup f(T)$
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
132971
Prove that $|a| < b \iff -b<a<b$
113411
If $E$ is generated by $E_1$ and $E_2$, then $[E:F]\leq [E_1:F][E_2:F]$?
35889
Suppose that f(0) = f(1) = 0 and x ∈ (0, 1). Prove that there exists c ∈ (0, 1) such that f'(c) = f(x).
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
62455
Prove Equivalence Relation in G
144589
Proving that if $f(x) \le g(x)$ then $f(x_0) \le g(x_0)$
142494
Functions $f(x)/g(x), g(x)/h(x),h(x)/f(x)$ are constant
105455
Prove that "injective function $f:X\to Y$ exists" and "surjective function $g:Y\to X$ exists" is logically equivalent.
40609
Prove that $f(X)$ and $g(Y)$ are independent if $X$ and $Y$ are independent
80009
Prove that $| |a|-|b| | \le |a-b|$