\[\boxed{\mathbf{2.}}\]
\[\textbf{а)}\ f\left( g(x) \right) = \sqrt{\lg x}\]
\[f(x) = \sqrt{x};\ \ g(x) = \lg x.\]
\[\textbf{б)}\ f\left( g(x) \right) = \ln x^{4};\]
\[f(x) = \ln x;g(x) = x^{4}.\]