The function  $f\left(x\right)$ is defined on the interval $\left[0,1\right]$. Find the domain of definition of the functions.

$f\left(\sin x\right)$

$y={\log }_{\sqrt{5}}\left(\sqrt{2}\left(\sin x-\cos x\right)+3\right)$

$f\left(x\right)=\frac{x^2+x+1}{x^2-x+1}$

Classify the following function $f\left(x\right)$ defined in $R\to R$ as injective, surjective, both or none

$f\left(x\right)=x^3+6x^2+11x+6$

Classify the following function $f\left(x\right)$ defined in $R\to R$ as injective, surjective, both or none

$f\left(x\right)=\left(x^2+x+5\right)\left(x^2+x-3\right)$