\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*} $ f(x) = x^2$
\end{equation*}
\end{document}
#And this is the error:
! Display math should end with $$.
l.11 $
?
Remove the $ signs from the line with your equation in it.
It should read
\begin{equation*} f(x) = x^2
I think.
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