Just as the title says, I really don't see how there's a missing brace anywhere. I'm a rookie with LaTeX so I don't know if there's some other cause for this kind of error. I have amsmath included for the align environment.
\documentclass{article}
\usepackage[margin=0.5in]{geometry}
\usepackage{amsfonts}
\usepackage{amsmath}
\begin{document}
\textbf{1.}\\
\begin{align}
(a) $f \circle g \circle h =& 2(\frac{\sqrt{x}}{1+\sqrt{x}})$\\
(b) $h \circle g \circle =& \sqrt{\frac{2x}{1+2x}}$\\
(c) $f \circle f =& 4x$\\
\end{align}
\end{document}

alignuses maths mode already so you don't want$signs. But\circlecan't be used in maths mode. What are you trying to do exactly? You should use\\in the first line. And it looks as if you are manually numbering things. Don't do that. People are useless at it. Computers are good at it. – cfr Mar 01 '16 at 03:40alignis a math mode environment and automatically sticks you in math mode.$signs, by and large, shouldn't appear anywhere within analignenvironment (I can think of the exception of entering text mode and then having maths within that:... \text{xyz $a + b$ pqr stu}). In other news I guess you're trying to make a list. This is actually quite a hard list to make, with the alignment as well (personally I'd probably sacrifice that) but you should do a little reading into how to make lists with LaTeX – Au101 Mar 01 '16 at 03:40\circwith\circlebecause I initially thought that was an issue. Thanks for the link and for the explanation of align, it makes much more sense now. – Alex Clough Mar 01 '16 at 03:43