User:Zhoujef000

test

1434

xonk (-1434 MOHS FE)

Find all functions $f: \mathbb{R} \to \mathbb{R}$ such that $f(xonkrbo)=xonkrbo$ for all real numbers $x,o,n,k,r,$ and $b.$

Let $A$ be the set of positive real numbers. Determine, with proof, if there exists at least one function $f : A\to A$ such that $f(x^x)=f(x)^{f(x)}$ for all real $x$ in $A.$

Determine all functions $f:\mathbb{R} \to \mathbb{R}$ such $f(x+y)=f(y)$ for all real numbers $x$ and $y.$

Find all functions $f:\mathbb{R}\to \mathbb{R}$ such that $f\left(x+\dfrac{1}{x}\right)+f\left(y+\dfrac{1}{y}\right)+f\left(z+\dfrac{1}{z}\right)=1$ for all real numbers $x,y,z\neq 0.$

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User:Zhoujef000

1434