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

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

(i) $f\left(x\right)\ne b$

(ii) $f\left(y\right)=b$

(iii) $f\left(z\right)\ne a$

Find the function $f$ (as ordered pair).

$f\left(x\right)=\log \left(x+\sqrt{1+x^2}\right)$

Find whether the following functions are even or odd or none:

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