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

• 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 $-f(x)$

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 $f^{-1}(x)$

• 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. – mdp 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.

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.