sigmoid $\circ$ sigmoid = sigmoid?

functions examples-counterexamples function-and-relation-composition

Define $g(x)=10\tanh(x/10)+\tanh(10x)$ and $f(x)=g(x-5)$.

$g(x)$:

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$g'(x):$

enter image description here

$g''(x):$

enter image description here

$f(g(x)):$

enter image description here

Note that despite how the graphs look, all derivatives are obviously bounded.

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