New posts in functions

Prove that $f[f^{-1} [f[X]]] = f[X]$

A problem on range of a trigonometric function: what is the range of $\frac{\sqrt{3}\sin x}{2+\cos x}$?

functions trigonometry

Physical interpretation and notions about conjugate function?

functions convex-analysis convex-optimization

What's the difference between "relation", "mapping", and "function"?

functions terminology definition

Solving functional equation $f(x+y)+f(x-y)=2f(x)\cos y$?

functions trigonometry functional-equations

About the addition formula $f(x+y) = f(x)g(y)+f(y)g(x)$

functions trigonometry arithmetic functional-equations

I am searching for an unusual real-valued function.

functions functional-equations

Arithmetic function to return lowest in-parameter

Is every injective function invertible?

calculus functions elementary-set-theory

Proving that $A\subseteq f^{-1}(f(A))$ and that if $f$ is injective $A=f^{-1}(f(A))$.

functions proof-verification

$f : \mathbb{R}^+ → \mathbb{R}$ with $f(0) = f'(0) = 0$ and $f(x) < x^2$ and $f',f'',f''' > 0$?

real-analysis functions derivatives

If $f(x) = \frac{x^3}{3} -\frac{x^2}{2} + x + \frac{1}{12}$, then $\int_{\frac{1}{7}}^{\frac{6}{7}}f(f(x))\,dx =\,$?

calculus integration functions definite-integrals

Grammar analysis: [We] [two brothers] are responsible for this act. [We] [both] are responsible for this act

grammar functions

What is the meaning of expressions of the type $f(\cdot)$ (function (dot))?

functions notation

Prove that $C = f^{-1}(f(C)) \iff f$ is injective and $f(f^{-1}(D)) = D \iff f$ is surjective

Can a continuous real function take each value exactly 3 times? [duplicate]

real-analysis functions

If $|A|=30$ and $|B|=20$, find the number of surjective functions $f:A \to B$.

combinatorics elementary-number-theory functions

Equation for a smooth staircase function

Generalization of $\lfloor \sqrt n+\sqrt {n+1}+\sqrt{n+2}+\sqrt{n+3}+\sqrt{n+4}\rfloor=\lfloor\sqrt {25n+49}\rfloor$

number-theory functions summation radicals ceiling-and-floor-functions

How to prove that there exist no functions $f,g:\Bbb{R}\to\Bbb{R}$ such that $f(g(x))=x^{2018}$ and $g(f(x))=x^{2019}$?

real-analysis calculus functions