Is there a bijective map from $(0,1)$ to $\mathbb{R}$?

I couldn't find a bijective map from $(0,1)$ to $\mathbb{R}$. Is there any example?

Here is a nice one ${}{}{}{}{}{}{}{}{}$, can you find the equation? enter image description here fg fgf gf gdddddfgfdgfgdgfgdfg

Here is a bijection from $(-\pi/2,\pi/2)$ to $\mathbb{R}$: $$ f(x)=\tan x. $$ You can play with this function and solve your problem.

$g(x)=\frac 1{1+e^x}$ gives a bijection from $\Bbb R$ to $(0,1)$, so take the inverse of this map.

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