Is there a mathematical symbol for "solution set of"?
ex:
"$5 \in \text{[solution set of] } f$", or "$0 \notin \text{[solution set of] } g(x) =x^2+x-2$"
[Math] Mathematical symbol for “solution set of”
notation
notation
Is there a mathematical symbol for "solution set of"?
ex:
"$5 \in \text{[solution set of] } f$", or "$0 \notin \text{[solution set of] } g(x) =x^2+x-2$"
Best Answer
If $f:X\to Y$ is a function, the set of all points $x\in X$ so that $f(x)=y\in Y$ is commonly denoted $f^{-1}(\{y\})$. So if $5$ is a solution to $f(x)=0$, we could write $$5\in f^{-1}(\{0\}).$$ Some authors will write this as $f^{-1}(y)$, (without brackets), but I don't like this because it could be confused with a reference to the inverse of $f$, which may not even exist.
In fact, if $S\subset Y$, we can write the set of all $x\in X$ so that $f(x)\in S$ as $f^{-1}(S)$. Such a set is called the preimage of $S$.