if $f(g(x))=x^3$ and $g(f(x))=x^4$ find $f(x)$ and $g(x)$
3922
How to prove that there exist no functions $f,g:\Bbb{R}\to\Bbb{R}$ such that $f(g(x))=x^{2018}$ and $g(f(x))=x^{2019}$?
60073
Proving $4(a^3 + b^3) \ge (a + b)^3$ and $9(a^3 + b^3 + c^3) \ge (a + b + c)^3$
76694
Proving that $UT=TU$ iff $U=g(T)$ for some polynomial $g$
13248
How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?
144589
Proving that if $f(x) \le g(x)$ then $f(x_0) \le g(x_0)$
19355
prove $f(x)=x^3+x$ is one to one and onto
144018
Integration by parts for f(x).g(x)
103706
If $\{f(0)\}^{2} + \{f'(0)\}^{2} = 4$ then there is a $c$ with $f(c) + f''(c) = 0$
80015
$Tr(A^2)=Tr(A^3)=Tr(A^4)$ then find $Tr(A)$
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
72251
$g\circ f$ is Surjective and $g$ is Injective then Prove that $f$ is surjective
100900
Finding maxima and minima of $f(x,y)= x^4 + y^4 - 2x^2 - 2y^2 + 4xy$
26207
If $f$ is a quadratic and $f(x)>0\;\forall x$, and $g= f + f' + f''$, prove $g(x)>0\; \forall x$
120960
$f,g$ such that $\int fg = \int f \int g$
46629
Prove if $f(x) = g(x)$ for each rational number x and $f$ and $g$ are continuous, then $f = g$
7858
Proving that $f(x)$ is irreducible over $F(b)$ if and only if $g(x)$ is irreducible over $F(a)$
56712
How can I find the domain and derivative of the function?