If $LaTeX: \displaystyle f(x)=\sqrt{x}$ and $LaTeX: \displaystyle g(x)=\frac{6}{4 x + 9}$ find $LaTeX: \displaystyle (f\circ g)(x)$ .

Evaluating $LaTeX: \displaystyle f(x)$ at $LaTeX: \displaystyle g(x)$ gives $LaTeX: \displaystyle (f\circ g)(x)=f(g(x))=\sqrt{6} \sqrt{\frac{1}{4 x + 9}}$ .