New posts in functions

Continuous $f : \mathbb R \to \mathbb R$ satisfying $f\left(\sqrt{\frac{x^2 + y^2}{2}}\right) = \frac{f(x) + f(y)}{2}$

functions contest-math functional-equations

Intuition behind Cantor-Bernstein-Schröder

functions elementary-set-theory intuition

Determining all $f : \mathbb R \to \mathbb R$ that satisfy $f\bigl(xf(y)\bigr) = x^{2002}f\bigl(f(y)\bigr)$

functions contest-math functional-equations

Solutions of the functional equation $f(x+1)= xf(x)$

functions functional-equations substitution

$f:\mathbb N_0\to\mathbb N_0$ with $2f\left(m^2+n^2\right)=f(m)^2+f(n)^2$ and $f\left(m^2\right)\geqslant f\left(n^2\right)$ when $m\geqslant n$

functions contest-math functional-equations

Showing $f$ constant if it is continuous and $f(2x) = f(x)$

functions solution-verification functional-equations

Determining all $f : \mathbb R \to \mathbb R$ that satisfy $xf(x) - yf(y) = (x-y)f(x+y)$

functions contest-math functional-equations

Does $f\big(x^2-y^2\big)=x\cdot f(x)-y\cdot f(y)$ imply $f\big(x^2\big)=x^2\cdot f(1)$?

limits functions functional-equations

How To Slice $Re(1/(1+z))$ Into A Cartesian Function For Any Angle?

functions complex-numbers terminology graphing-functions

Terminology Question: Precompose vs Compose?

functions terminology

Do you know this function?

real-analysis limits functions

Prove that continuous functions mapping irrationals to rationals must be constant

functions elementary-set-theory

Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $

real-analysis functions continuity

Why $f^{-1}(f(A)) \not= A$ [duplicate]

elementary-set-theory functions

Solve these functional equations: $\int_0^1\!{f(x)^2\, \mathrm{dx}}= \int_0^1\!{f(x)^3\, \mathrm{dx}}= \int_0^1\!{f(x)^4\, \mathrm{dx}}$

functions definite-integrals functional-equations integral-equations

How many non-differentiable functions exist?

real-analysis functions elementary-set-theory derivatives cardinals

Is the limit of $f(n) = n-n$ zero as $n\rightarrow \infty$?

limits functions

Intuitively, why are the curves of exponential, log, and parabolic functions all smooth, even though the gradient is being changed at every point?

algebra-precalculus functions

Recursive definition of hyperbolic functions

real-analysis functions recursion

Find all strictly monotone $f:(0,+\infty) \to (0, +\infty)$ such that $f(\frac{x^2}{f(x)})=x.$

real-analysis functions functional-equations