# tanh &#x2061;<!-- ⁡ --> ( x + y ) = tanh &#x2061;<!-- ⁡ --> ( z ) &#x21

$\mathrm{tanh}\left(x+y\right)=\mathrm{tanh}\left(z\right)\to x+y=z?$?
Why is this true?
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bideanbarrenaf5
$\frac{\mathrm{d}}{\mathrm{d}x}\mathrm{tanh}\left(x\right)={\mathrm{sech}}^{2}\left(x\right)>0$
So $\mathrm{tanh}\left(x\right)$ is strictly increasing, hence injective.