Is there a symbol used for an element which a function sends to zero?
Like this: $f(?) = 0$, where "$?$" would be the symbol for which I am wondering if exists.
I think this could be useful for instance in factoring polynomials: $ax^2+bx+c = a(x-?_1)(x-?_2)$ and the zeroes of functions are always interesting.
Best Answer
You could write $f^{-1}(0)$. But note that this is a set, not a single specific value, because there might be several different values that the function $f$ sends to zero.
Another notation you might see is $Z(f)$, standing for the "zero set" of $f$: $$ Z(f) = \{ x : f(x)=0\} $$
In some fields, like linear algebra, $Z(f)$ is called the "kernel" of $f$. See here.
Personally, I don't like using special symbols when words will serve instead. So, in my view, "$x$ is a zero of $f$" is much better than "$x \in Z(f)$". Of course, "$f(x)=0$" is pleasantly clear and concise, too.