Function/x over modulus x +1/Continuous bijection/R and open interval/Exercise

Show that the function defined by

${}f(x)={\frac {x}{\vert {x}\vert +1}}\,$

is a continuous, strictly increasing, bijective function

$f\colon \mathbb {R} \longrightarrow {]{-1},1[}$

and that its inverse function is also continuous.

Create a solution