# What do you call $-f(x)$

I have a terminology question. I am referring to a sigmoid (S-shape function) in a paper however it is inverted (if the sigmoid is $f(x)$, my function $-f(x)$).

I initially wanted to refer to it as an inverse sigmoid... but I think that would refer to $f^{-1}(x)$ ?

Any help welcome! thank you

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I do not think "inverted sigmoid" would refer to $f^{-1}(x)$. Maybe "inverse sigmoid" would, but even that probably needs more explanation before using it. – GEdgar Nov 8 '12 at 15:57
good point, I edited the post – John Nov 9 '12 at 12:18
Another option could be additive inverse. – Pedro Tamaroff Dec 8 '12 at 2:34

I suppose that negated is the right name: $f(x)$ negated is $-f(x)$

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If you multiplied by $-1$ then the symbol is $-f(x)$. If you found the inverse function (then the composition is the identity) then the symbol is $f^{-1}(x)$

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hi tota, thanks for your input. My question is actually, how do you call -f? – John Nov 8 '12 at 12:45
We call in mathematics the "opossite function " I think, (my tongue language is sapnish, in spanish we call the "opuesta" – tota Nov 8 '12 at 13:21
opposit is the correct term for an additive inverse in all algebraic structure with an addition. – tota Nov 8 '12 at 13:41
I am not familiar with this terminology, although I think I would probably guess correctly what was meant. "Opposite sigmoid" is a perfectly good name, but I would advise you to explain in the paper what you mean by it. – Matthew Pressland Nov 8 '12 at 13:43

I agree with graziano governatori that "negated sigmoid" is a good name.

Another possibility is "reflected sigmoid".

But as Matt Pressland wrote, whatever terminology you chose in the end you should clearly define it.

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It depends on what you want to stress. If you only mean a left-right flipped S shape, I think it is usually called a "negative sigmoid" (example 1 on p.4, example 2, example 3 on p.4). However, logistic-like functions with negative parameters such as $1/(1+e^{-(-x)})$ are also called negative sigmoids. Certainly, such functions can be written in the form of $$\mathtt{constant} + \mathtt{negative\ multiple} * \mathtt{some\ sigmoid}(x),$$ but the stress here is the shape of the curve rather the negative multiple itself.

If you want to stress that the function is constructed by multiplying a sigmoid function by a negative number, I don't know the proper name, but I agree with the others here that "negated sigmoid" is a good name. Yet, a google search on "negated sigmoid" returns only 25 results. So this is perhaps not a very common name.

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