Newbetuts

$f$ differentiable, $f(x)$ rational if $x$ rational; $f(x)$ irrational if $x$ irrational. Is $f$ a linear function?

Continuous function that take irrationals to rationals and vice-versa. [duplicate]

Are there continuous functions $f,g:\mathbb{R}\longrightarrow\mathbb{R}$ such that for any $x$, $f(g(x))=\sin x$ and $g(f(x))=\cos x$?

Regularity of the function $|x|^ax$

If $f(x)^2=x+(x+1)f(x+2)$, what is $f(1)$?

A question about showing that an injective map $f$ between finite sets of same cardinality is surjective. [duplicate]

Seemingly conflicting notions of a function

A function satisfying $f(\frac1{x+1})\cdot x=f(x)-1$ and $f(1)=1$?

Description of the function graph

Change of order of double limit of function sequence

Any partition of $\{1,2,\ldots,100\}$ into seven subsets yields a subset with numbers $a,b,c,d$ such that $a+b=c+d$. [closed]

Prove: For odd integers $a$ and $b$, the equation $x^2 + 2 a x + 2 b = 0$ has no integer or rational roots.

Finding the maximum and minimum values of $f(x)=a^x+a^{1/x}$

If $\frac{f(x^2)}{f(x)}=1+x+x^2+\ldots+x^7$ then what is $f(x)$?

How can you factor $x^4-6x^3+8x^2+2x-1?$

New posts in functions

What is the inverse of $2^x$? [duplicate]

Does $f(x) \in \mathbb{Z}[x]$ irreducible, imply $f(2x)$ also irreducible?

What does $F(\varphi)(z)$ mean?

A function that grows faster than any function in the sequence $e^x, e^{e^x}, e^{e^{e^x}}$...

Is any divergence-free curl-free vector field necessarily constant?

$f$ differentiable, $f(x)$ rational if $x$ rational; $f(x)$ irrational if $x$ irrational. Is $f$ a linear function?

Continuous function that take irrationals to rationals and vice-versa. [duplicate]

Are there continuous functions $f,g:\mathbb{R}\longrightarrow\mathbb{R}$ such that for any $x$, $f(g(x))=\sin x$ and $g(f(x))=\cos x$?

Regularity of the function $|x|^ax$

If $f(x)^2=x+(x+1)f(x+2)$, what is $f(1)$?

A question about showing that an injective map $f$ between finite sets of same cardinality is surjective. [duplicate]

Seemingly conflicting notions of a function

A function satisfying $f(\frac1{x+1})\cdot x=f(x)-1$ and $f(1)=1$?

Description of the function graph

Change of order of double limit of function sequence

Any partition of $\{1,2,\ldots,100\}$ into seven subsets yields a subset with numbers $a,b,c,d$ such that $a+b=c+d$. [closed]

Prove: For odd integers $a$ and $b$, the equation $x^2 + 2 a x + 2 b = 0$ has no integer or rational roots.

Finding the maximum and minimum values of $f(x)=a^x+a^{1/x}$

If $\frac{f(x^2)}{f(x)}=1+x+x^2+\ldots+x^7$ then what is $f(x)$?

How can you factor $x^4-6x^3+8x^2+2x-1?$