Find whether the function $f\left(x\right)=x+\frac{1}{x}, x\in \left(0,\infty \right)$, is one-one or many-one & into or onto if $f:D\to R$, where $D$, is its domain.

Find whether the function is one-one or many-one & into or onto if $f:D\to R$ where $D$ is its domain.

$f\left(x\right)=\sqrt{1-e^{\left(\frac{1}{x}-1\right)}}$

Find whether the function is one-one or many-one & into or onto if $f:D\to R$ where $D$ is its domain.

$f\left(x\right)=\frac{3x^2}{4\pi }-\mathrm{cos\pi }x$

Find whether the function is one-one or many-one & into or onto if $f:D\to R$ where $D$ is its domain.

$f\left(x\right)=\frac{1+x^6}{x^3}$

Find whether the function $f\left(x\right)=x\cos x$, is one-one or many-one & into or onto if $f:D\to R$, where D is its domain.

Find whether the function is one-one or many-one & into or onto if $f:D\to R$ where $D$ is its domain.

$f\left(x\right)=\frac{1}{\sin \sqrt{\left|x\right|}}$

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

$f\left(x\right)=x\left|x\right|$

Classify the function $f\left(x\right)=\frac{x^2}{1+x^2}$, defined in $R\to R$, as injective, surjective, both or none.

Classify the function $f\left(x\right)=x^3-6x^2+11x-6$, defined in $R\to R$, as injective, surjective, both or none.